spreadsheet modelling in corporate finance - part 1 - time value of money

NET PRESENT VALUE General Discount Rate

InputsPeriod 0 1 2 3 4Current Investment 100.00 Future Cash Flows 21.00 34.00 40.00 33.00 Discount Rate 8.00% 7.60% 7.30% 7.00%

Net Present Value using a Time LinePeriod 0 1 2 3 4Cumulative Discount Factor 0.00% 8.00% 16.20% 24.70% 33.40%Cash Flows (100.00) 21.00 34.00 40.00 33.00 Present Value of Each Cash Flow (100.00) 19.44 29.26 32.08 24.73 Net Present Value 17.42

General Discount Rate

5

17.00 7.00%

542.80%

17.00 11.91

Symbol List All Corporate Finance Versions

Brealy Bringham Gitman Keown Ross

Bonds

Annual Coupon Rate CR CR CR CR CR CR

Yield To Maturity (Annualized) y y kd y kb y

Number of Payments / Period NOP NOP NOP NOP NOP NOP

Number of Periods to Maturity n N N n T T

Face value FV M M M M F

Discount Rate / Period I r. DR kd DR r.

Coupon Payment PMT C. INT I I C.

Bond Price PV PV VB B0 Vb PV

Forward Rate from T-1 to T fn fn FRT-1,T fn fT-1,T fn

Capital Structure

Value of the Firm V V V V V V

Debt D D D D D B

Equity E E E E E S

Face Value of Debt B B B B B D

Black-Scholes Option Pricing

Stock Price S P P S S S

Exercise Price E EX X E E E

Riskfree Rate r r kRF r r r

Volatility

Time to Maturity T t t T T t

d1 d1 d1 d1 d1 d1 d1

d2 d2 d2 d2 d2 d2 d2

N(d1) N(d1) N(d1) N(d1) N(d1) N(d1) N(d1)

N(d2) N(d2) N(d2) N(d2) N(d2) N(d2) N(d2)

Call Price C C V C C C

Put Price P Put Put P P P

Dividend Yield d d d d d d

Bodie-Merton

CR

r.

NOP

n

M

DR

C.

P

nr1

V

B

S

D

Vs

E

r

t

d1

d2

N(d1)

N(d2)

V0

Vp

d

Van Horne

SINGLE CASH FLOW Present Value

InputsSingle Cash Flow $1,000.00Discount Rate / Period 6.0%Number of Periods 5

Present Value using a Time LinePeriod 0 1 2 3 4Cash Flows $0.00 $0.00 $0.00 $0.00 $0.00Present Value of Each Cash Flow $0.00 $0.00 $0.00 $0.00 $0.00

Present Value $747.26

Present Value using the Formula $747.26

Present Value using the PV formula $747.26

Present Value

5$1,000.00

$747.26

Present Value of Each Cash Flow = (Cash Flow) / ((1 + Discount Rate/Period) ^ Period)

Present Value = (Cash Flow) / ((1 + Discount Rate/Period) ^ Period)

=-PV(Discount Rate / Period, Number of Periods, 0, Single Cash Flow)

Problem. A single cash flow of $1,000.00 will be received in 5 periods. For this cash flow, the appropriate discount rate / period is 6.0%. What is the present value of this single cash flow?

SINGLE CASH FLOW Present Value

InputsSingle Cash Flow $1,673.48Discount Rate / Period 7.8%Number of Periods 4

Present Value using a Time LinePeriod 0 1 2 3 4Cash Flows $0.00 $0.00 $0.00 $0.00 $1,673.48Present Value of Each Cash Flow $0.00 $0.00 $0.00 $0.00 $1,239.21Present Value $1,239.21

Present Value using the Formula $1,239.21

Present Value using the PV formula $1,239.21

Present ValueProblem. A single cash flow of $1,673.48 will be received in 4 periods. For this cash flow, the appropriate discount rate / period is 7.8%. What is the present value of this single cash flow?

SINGLE CASH FLOW Future Value

InputsSingle Cash Flow $747.26Discount Rate / Period 6.0%Number of Periods 5

Present Value using a Time LinePeriod 0 1 2 3 4Cash Flows $747.26 $0.00 $0.00 $0.00 $0.00Future Value of Each Cash Flow $1,000.00 $0.00 $0.00 $0.00 $0.00

Future Value

Future Value using the Formula $1,000.00

Future Value using the PV formula $1,000.00

Future Value

5$0.00$0.00

$1,000.00

Future Value of Each Cash Flow = (CashRate/Period)^((Number of Periods) - (Current Period))

Future = (Cash Flow) * (1 + Discount Rate/Period)^(Number of Periods)

=-FV(Discount Rate / Period, Number of Periods, 0, Single Cash Flow)

Problem. A single cash flow of $747.25 is available now (in period 0). For this cash flow, the appropriate

discount rate / period is 6.0%. What is the period 5 future value of this single cash flow?

SINGLE CASH FLOW Future Value


Present Value using a Time LinePeriod 0 1 2 3 4Cash Flows $932.47 $0.00 $0.00 $0.00 $0.00Future Value of Each Cash Flow $1,086.67 $0.00 $0.00 $0.00 $0.00Future Value $1,086.67

Future Value using the Formula $1,086.67

Future Value using the PV formula $1,086.67

Future Value

Problem. A single cash flow of $932.47 is available now (in period 0). For this cash flow, the appropriate discount rate / period is 3.9%. What is the period 4 future value of this single cash flow?

ANNUITY Present Value

InputsPayment $80.00Discount Rate / Period 6.0%Number of Periods 5

Annuity Present Value using a Time LinePeriod 0 1 2 3 4Cash Flows $0.00 $80.00 $80.00 $80.00 $80.00Present Value of Each Cash Flow $0.00 $75.47 $71.20 $67.17 $63.37


Annuity Present Value using the Formula $336.99

Annuity Present Value using the PV formula $336.99

n

i=1

n

i=1

Sn = 1 + x1 + x2 +…+ xn | *x

∑P / (1 + DR)n = P / (1 + DR)1 + P / (1 + DR)2

x* Sn = x + x2 +…+ xn + xn+1 =>

= P / (1 + DR) (1 + (1 + DR)

x* Sn = 1 + x + x2 +…+ xn + xn+1 – 1 =>

1 / (1 + DR) = k => P * k (1 + k + k2 + … + kn

x* Sn = Sn + xn+1 – 1

Sn*(x - 1) = (xn+1 – 1)

∑P / (1 + DR)n = P / (1 + DR) * (1 - 1 / (1 + DR)

Sn = (xn+1 – 1) / (x - 1) | *(-1)

= P * (1 - (1 + DR)-n)) / DR

Sn = (1 - xn+1) / (1 - x)

Present Value

5$80.00$59.78


=-PV(Discount Rate / Period, Number of Periods, Payment, 0)

Problem. An annuity pays $80.00 each period for 5 periods. For these cash flows, the appropriate discount rate / period is 6.0%. What is the present value of this annuity?

Annuity Present Value = (Payment) * (1 - ((1 + Discount Rate/Period) ^ (-Number of Periods))) / (Discount Rate/Period)

+ P / (1 + DR)2 + P / (1 + DR)3 + … + P / (1 + DR)n =

= P / (1 + DR) (1 + (1 + DR)1 + (1 + DR)2 + … + (1 + DR)n-1)

1 / (1 + DR) = k => P * k (1 + k + k2 + … + kn ) = P * k * (1 - kn+1) / (1 - k) =>

= P / (1 + DR) * (1 - 1 / (1 + DR)n) * ( 1 - 1 / (1 + DR)) =

ANNUITY Future Value


Future Value using a Time LinePeriod 0 1 2 3 4 5Cash Flows $0.00 $80.00 $80.00 $80.00 $80.00 $80.00Future Value of Each Cash Flow $0.00 $101.00 $95.28 $89.89 $84.80 $80.00

Future Value $450.97

Future Value using the Formula $450.97

Future Value using the PV formula $450.97

0.483% 5.79%

$63,780.27

n

∑P * (1 + DR)n-i = P * (1 + DR)n-1 + P * (1 + DR)n-2 + … + P * (1 + DR)0 =

i=1

= P ((1 + DR)n-1 + (1 + DR)n-2 + … + 1) =

= P ((1+DR)n – 1) / DR

=-FV(Discount Rate / Period, Number of Periods, Payment, 0)

Problem. An annuity pays $80.00 each period for 5 periods. For these cash flows, the appropriate discount rate / period is 6.0%. What is the period 5 future value of this annuity?

Future Value of Each Cash Flow = (Cash Flow) * (1 + Discount Rate/Period)^((Number of Periods) - (Current Period))

Annuity Future Value = (Payment) * (((1 + Discount Rate/Period) ^ (Number of Periods)) - 1) / (Discount Rate/Period)

+ P * (1 + DR)n-2 + … + P * (1 + DR)0 =

+ (1 + DR)n-2 + … + 1) =

ANNUITY System of 4 Annuity Variables

InputsPayment $80.00Discount Rate / Period 6.0%Number of Periods 5 Present Value $336.99

Payment

Payment using the formula $80.00Payment using the PMT function $80.00

Discount Rate / PeriodDiscount Rate / Per using the RATE functio 6.0%

Number of PeriodsNumber of Periods using NPER function 5

Present Value using a Time LinePeriod 0 1 2 3 4 5Cash Flows $0.00 $80.00 $80.00 $80.00 $80.00 $80.00Present Value of Each Cash Flow $0.00 $75.47 $71.20 $67.17 $63.37 $59.78




=PMT(Discount Rate / Period, Number of Periods, -Present Value, 0)

=RATE(Number of Periods, Payment, -Present Value, 0)

=NPER(Discount Rate / Period, Payment, -Present Value, 0)



Problem. There is a tight connection between all of the inputs and output to annuity valuation. Indeed,

they form a system of four annuity variables: (1) Payment, (2) Discount Rate / Period, (3) Number of

Periods, and (4) Present Value. Given any three of these variables, find the fourth variable.

Payment = (Present Value) / ((1 - ((1 + Discount Rate/Period) ^ (-Number of Periods))) / (Discount Rate/Period))



InputsPayment $142.38Discount Rate / Period 4.5%Number of Periods 6 Present Value $734.38

Payment




Present Value using a Time LinePeriod 0 1 2 3 4 5Cash Flows $0.00 $142.38 $142.38 $142.38 $142.38 $142.38Present Value of Each Cash Flow $0.00 $136.25 $130.38 $124.77 $119.39 $114.25




=PMT(Discount Rate / Period, Number of Periods, -Present Value, 0)

=RATE(Number of Periods, Payment, -Present Value, 0)

=NPER(Discount Rate / Period, Payment, -Present Value, 0)

6$142.38$109.33


Problem. An annuity pays $142.38 each period for 6 periods. For these cash flows, the

appropriate discount rate / period is 4.5%. What is the present value of this annuity?

Payment = (Present Value) / ((1 - ((1 + Discount Rate/Period) ^ (-Number of Periods))) / (Discount Rate/Period))

Present Value of Each Cash Flow = (Cash Flow) / ((1 + Discount Rate/Period) ^

Period)



InputsPayment $63.92Discount Rate / Period 9.1%Number of Periods 4 Future Value $292.75

Payment




Future Value using a Time LinePeriod 0 1 2 3 4Cash Flows $0.00 $63.92 $63.92 $63.92 $63.92Future Value of Each Cash Flow $0.00 $83.01 $76.08 $69.74 $63.92

Future Value $292.75

Future Value using the Formula $292.75

Future Value using the PV formula $292.75

=PMT(Discount Rate / Period, Number of Periods, -Future Value, 0)

=RATE(Number of Periods, Payment, -Future Value, 0)

=NPER(Discount Rate / Period, Payment, -Future Value, 0)

=-FV(Discount Rate / Period, Number of Periods, Payment, 0)

Problem. An annuity pays $63.92 each period for 4 periods. For these cash flows, the appropriate discount rate / period is 9.1%. What is the period 5 future value of this annuity?

Payment = Future Value /((((1 + Discount Rate/Period) ^ (Number of Periods)) - 1) / (Discount Rate/Period))

Future Value of Each Cash Flow = (Cash Flow) * (1 + Discount Rate/Period)^((Number of Periods) - (Current Period))

Annuity Future Value = (Payment) * (((1 + Discount Rate/Period) ^ (Number of Periods)) - 1) / (Discount Rate/Period)

NET PRESENT VALUE Constant Discount Rate

InputsDiscount Rate 8.0%Period 0 1 2 3 4 Current Investment $100.00Future Cash Flows $21.00 $34.00 $40.00 $33.00

Net Present Value using a Time LinePeriod 0 1 2 3 4Cash Flows ($100.00) $21.00 $34.00 $40.00 $33.00 Present Value of Each Cash Flow ($100.00) $19.44 $29.15 $31.75 $24.26

Net Present Value $16.17

Present Value using the NPV functionNet Present Value $16.17

Constant Discount Rate

5

$17.00

5$17.00 $11.57

Present Value of Each Cash Flow = (Cash Flow) / ((1 + Discount Rate) ^ Period)

=-(Current Investment) + NPV(Discount Rate, Future Cash Flows)

Problem. A project requires a current investment of $100.00 and yields future expected cash flows of $21.00, $34.00, $40.00, $33.00, and $17.00 in periods 1 through 5, respectively. All figures are in thousands of dollars. For these expected cash flows, the appropriate discount rate is 8.0%. What is the net present value of this project?

NET PRESENT VALUE Constant Discount Rate

InputsDiscount Rate 6.3%Period 0 1 2 3 4 Current Investment $189.32Future Cash Flows $45.19 $73.11 $98.54 $72.83





5

$58.21

5$58.21 $42.89



Problem. A project requires a current investment of $189.32 and yields future expected cash flows of $45.19, $73.11, $98,54, $72.83, and $58.21 in periods 1 through 5, respectively. All figures are in thousands of dollars. For these expected cash flows, the appropriate discount rate is 6.3%. What is the net present value of this project?


InputsPeriod 0 1 2 3 4 Current Investment $100.00Future Cash Flows $21.00 $34.00 $40.00 $33.00Discount Rate 8.0% 7.6% 7.3% 7.0%

Net Present Value using a Time LinePeriod 0 1 2 3 4

Cumulative Discount Factor 8.0% 16.2% 24.7% 33.4%

Cash Flows ($100.00) $21.00 $34.00 $40.00 $33.00

Present Value of Each Cash Flow ($100.00) $19.44 $29.26 $32.08 $24.73



5

$17.007.0%

5

42.8%

$17.00

$11.91

Problem. A project requires a current investment of $100.00 and yields future expected cash flows

of $21.00, $34.00, $40.00, $33.00, and $17.00 in periods 1 through 5, respectively. All figures are in

thousands of dollars. For these expected cash flows, the appropriate discount rate starts at 8.0% in

period 1 and declines to 7.0% in period 5. What is the net present value of this project?

Cumulative Discount Factor on date t = (1 + Cumulative Discount Factor on date t-1) * (1 + Discount Rate on date t) - 1

Present Value of Each Cash Flow = (Cash Flow on date t) / (1+ Cumulative Discount Factor on date t)


InputsPeriod 0 1 2 3 4 Current Investment $54.39Future Cash Flows $19.27 $27.33 $34.94 $41.76Discount Rate 6.4% 6.2% 5.9% 5.6%

Net Present Value using a Time LinePeriod 0 1 2 3 4

Cumulative Discount Factor 6.4% 12.9% 19.6% 26.4%

Cash Flows ($54.39) $19.27 $27.33 $34.94 $41.76

Present Value of Each Cash Flow ($54.39) $18.11 $24.20 $29.21 $33.05



5

$32.495.4%

5

33.2%

$32.49

$24.39

Problem. A project requires a current investment of $54.39 and yields future expected cash flows of

$19.27, $27.33, $34.94, $41.76, and $32.49 in periods 1 through 5, respectively. All figures are in

thousands of dollars. For these expected cash flows, the appropriate discount rate starts at 6.4% in

period 1 and declines to 5.4% in period 5. What is the net present value of this project?


Present Value of Each Cash Flow = (Cash Flow on date t) / (1+ Cumulative Discount Factor on date t)

REAL & INFLATION Constant Discount Rate

InputsInflation Rate 3.0%Real Discount Rate 5.0%Period 0 1 2 3 4 Current Investment $100.00Future Cash Flows $21.00 $34.00 $40.00 $33.00

OutputsNominal Discount Rate 8.2%





5

$17.00

5$17.00 $11.49

(Nominal) Discount Rate = (1 + Inflation Rate) * (1 + Real Discount Rate) - 1





2 thousands of dollars. The inflation rate is 3.0%. For these expected cash flows, the appropriate

Real Discount Rate is 5.0%. What is the net present value of this project?

REAL & INFLATION Constant Discount Rate

InputsInflation Rate 2.7%Real Discount Rate 8.6%Period 0 1 2 3 4 Current Investment $117.39Future Cash Flows $38.31 $48.53 $72.80 $96.31

OutputsNominal Discount Rate 11.5%





5

$52.18

5$52.18 $30.23




Problem. A project requires a current investment of $117.39 and yields future expected cash flows of $38.31, $48.53, $72.80, $96.31, and $52.18 in periods 1 through 5, respectively. All figures are in thousands of dollars. The inflation rate is 2.7%. For these expected cash flows, the appropriate Real Discount Rate is 8.6%. What is the net present value of this project?

REAL & INFLATION General Discount Rate

InputsPeriod 0 1 2 3 4 Current Investment $100.00Future Cash Flows $21.00 $34.00 $40.00 $33.00Inflation Rate 3.0% 2.8% 2.5% 2.2%Real Discount Rate 5.0% 5.5% 6.0% 6.5%

Net Present Value using a Time LinePeriod 0 1 2 3 4Nominal Discount Rate 8.2% 8.5% 8.7% 8.8%

Cumulative Discount Rate 8.2% 17.3% 27.4% 38.7%

Cash Flows ($100.00) $21.00 $34.00 $40.00 $33.00

Present Value of Each Cash Flow ($100.00) $19.42 $28.99 $31.39 $23.79 Net Present Value $14.87


5

$17.002.0%6.5%

58.6%

50.7%

$17.00

$11.28




thousands of dollars. The forecasted inflation rate starts at 3.0% in period 1 and declines to 2.0% in

period 5. For these expected cash flows, the appropriate REAL discount rate starts at 5.0% in

period 1 and increases to 6.5% in period 5. What is the net present value of this project?


REAL & INFLATION General Discount Rate

InputsPeriod 0 1 2 3 4 Current Investment $328.47Future Cash Flows $87.39 $134.97 $153.28 $174.99Inflation Rate 3.4% 3.7% 4.0% 4.3%Real Discount Rate 7.8% 7.2% 6.6% 6.0%

Net Present Value using a Time LinePeriod 0 1 2 3 4Nominal Discount Rate 11.5% 11.2% 10.9% 10.6%

Cumulative Discount Rate 11.5% 23.9% 37.4% 51.9%

Cash Flows ($328.47) $87.39 $134.97 $153.28 $174.99

Present Value of Each Cash Flow ($328.47) $78.40 $108.92 $111.58 $115.22 Net Present Value $137.21


5

$86.414.7%5.4%

510.4%

67.6%

$86.41

$51.56



of $87.39, $134.97, $153.28, $174.99, and $86.41 in periods 1 through 5, respectively. All figures

are in thousands of dollars. The forecasted inflation rate starts at 3.4% in period 1 and increases to

4.7% in period 5. For these expected cash flows, the appropriate REAL discount rate starts at 7.8%

in period 1 and decreases to 5.4% in period 5. What is the net present value of this project?


Loan Amortization Basics

InputsPresent Value $300,000Interest Rate / year 8.00%Number of years 30

OutputsYear 1 2 3 4 5Beg. Principal Balance $300,000 $297,352 $294,492 $291,403 $288,067

Payment $26,648 $26,648 $26,648 $26,648 $26,648

Interest Component $24,000 $23,788 $23,559 $23,312 $23,045

Principle Component $2,648 $2,860 $3,089 $3,336 $3,603

Basics

6 31$284,464 ($0)

$26,648

$22,757

$3,891

=PMT(Interest Rate / Year, Number of Years, -Present Value, 0)

Principal Component in year t = Payment - (Interest Component)

Problem. To purchase a house, you take out a 30 year mortgage. The present value (loan amount) of the mortgage is $300,000. The mortgage charges an interest rate / year of 8.00%. What is the annual payment required by this mortgage? How much of each year's payment goes to paying interest and how much reducing the principal balance?

Interest Component in year t = (Interest rate/year) * (Beginning Principal Balance in year t)

Loan Amortization Sensitivity Analysis

InputsPresent Value $300,000Interest Rate / year 8.00%Number of years 30

OutputsYear 1 2 3 4 5 6 7Beg. Principal Balance $300,000 $297,352 $294,492 $291,403 $288,067 $284,464 $280,573

Payment $26,648 $26,648 $26,648 $26,648 $26,648 $26,648 $26,648

Interest Component $24,000 $23,788 $23,559 $23,312 $23,045 $22,757 $22,446

Principle Component $2,648 $2,860 $3,089 $3,336 $3,603 $3,891 $4,202

Data Table: Sensitivity of the Interest Component to the Interest Rate/ YearInput Values for Output formula: Interest ComponentInterest rate / year $24,000 $23,788 $23,559 $23,312 $23,045 $22,757 $22,446

7.00% $21,000 $20,778 $20,540 $20,285 $20,013 $19,722 $19,410 8.00% $24,000 $23,788 $23,559 $23,312 $23,045 $22,757 $22,446

Data Table: Sensitivity of the Principal Component to the Interest Rate/ YearInput Values for Output formula: Principal ComponentInterest rate / year $2,648 $2,860 $3,089 $3,336 $3,603 $3,891 $4,202

7.00% $3,176 $3,398 $3,636 $3,891 $4,163 $4,454 $4,766 8.00% $2,648 $2,860 $3,089 $3,336 $3,603 $3,891 $4,202

8 9 10 11 12 13 14 15 16$276,370 $271,832 $266,930 $261,636 $255,919 $249,744 $243,076 $235,873 $228,095

$26,648 $26,648 $26,648 $26,648 $26,648 $26,648 $26,648 $26,648 $26,648

$22,110 $21,747 $21,354 $20,931 $20,474 $19,980 $19,446 $18,870 $18,248

$4,539 $4,902 $5,294 $5,717 $6,175 $6,669 $7,202 $7,778 $8,401

$22,110 $21,747 $21,354 $20,931 $20,474 $19,980 $19,446 $18,870 $18,248 $19,076 $18,719 $18,337 $17,928 $17,491 $17,023 $16,522 $15,987 $15,413 $22,110 $21,747 $21,354 $20,931 $20,474 $19,980 $19,446 $18,870 $18,248

$4,539 $4,902 $5,294 $5,717 $6,175 $6,669 $7,202 $7,778 $8,401 $5,100 $5,457 $5,839 $6,248 $6,685 $7,153 $7,653 $8,189 $8,762 $4,539 $4,902 $5,294 $5,717 $6,175 $6,669 $7,202 $7,778 $8,401

17 18 19 20 21 22 23 24 25$219,694 $210,622 $200,823 $190,241 $178,812 $166,469 $153,138 $138,741 $123,192

$26,648 $26,648 $26,648 $26,648 $26,648 $26,648 $26,648 $26,648 $26,648

$17,576 $16,850 $16,066 $15,219 $14,305 $13,317 $12,251 $11,099 $9,855

$9,073 $9,798 $10,582 $11,429 $12,343 $13,331 $14,397 $15,549 $16,793

$17,576 $16,850 $16,066 $15,219 $14,305 $13,317 $12,251 $11,099 $9,855 $14,800 $14,144 $13,442 $12,690 $11,886 $11,026 $10,105 $9,120 $8,066 $17,576 $16,850 $16,066 $15,219 $14,305 $13,317 $12,251 $11,099 $9,855

$9,073 $9,798 $10,582 $11,429 $12,343 $13,331 $14,397 $15,549 $16,793 $9,376 $10,032 $10,734 $11,486 $12,290 $13,150 $14,071 $15,056 $16,109 $9,073 $9,798 $10,582 $11,429 $12,343 $13,331 $14,397 $15,549 $16,793

26 27 28 29 30 31$106,399 $88,262 $68,675 $47,521 $24,674 ($0)

$26,648 $26,648 $26,648 $26,648 $26,648

$8,512 $7,061 $5,494 $3,802 $1,974

$18,136 $19,587 $21,154 $22,847 $24,674

$8,512 $7,061 $5,494 $3,802 $1,974 $6,939 $5,732 $4,441 $3,060 $1,582 $8,512 $7,061 $5,494 $3,802 $1,974

$18,136 $19,587 $21,154 $22,847 $24,674 $17,237 $18,444 $19,735 $21,116 $22,594 $18,136 $19,587 $21,154 $22,847 $24,674

Problem. Examine the same 30 year mortgage for $300,000 as in the previous section.

Consider what would happen if the interest rate / year dropped from 8.00% to 7.00%. How

much of each year's payment goes to paying interest vs. how much goes to reducing the

principal under the two interest rates?

0 5 10 15 20 25 30 35$0

$5,000

$10,000

$15,000

$20,000

$25,000

$30,000

Principal And Interests Payments Over Time

7% Interest Component 8% Interest Component 7% Principal Component 8% Principal Component

Time (Years)

Pri

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pa

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nd

In

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spreadsheet modelling in corporate finance - part 1 - time value of money

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