powerpoint presentation · pmt(rate, nper, pv, [fv], [type]) rate the interest rate for the loan....

Excel [email protected]

[email protected]

Lecture 10 Financial Functions

• Negative numbers = cash you pay out, such as deposits to savings.

• Positive numbers = cash you receive, such as salary.

• PV – Present(Today’s) value.

• FV – just the number you get in future.

– FV = 100 is a value in future that is less than 100 today.

• If I deposit V today (9% FD for 5 years), how much can I get after Y years with fixed interest rate of r%.

After Y years = Capital * Rate * years

Payment Functions

PMT,IPMT,CUMIPMT,PPMT,ISPMT

PMT - PAYMENT function

• payment of a loan based on constant payments and a fixed interest rate.

• With the PMT function we can also calculate how much money we need to deposit each month in order to save X amount of money in X amount of years.

• how we can save 30.0000€ in 5 years, with an interest rate of 6%.

PMT(rate, nper, pv, [fv], [type])Rate The interest rate for the loan.

Nper The total number of payments for the loan.

Pv The present value, or the total amount that a series of future payments is worth now; also known as the principal.

Fv Optional. The future value, or a cash balance you want to attain after the last payment is made. If fv is omitted, it is assumed to be 0 (zero), that is, the future value of a loan is 0.

Type Optional. The number 0 (zero) (end) or 1(beginning) and indicates when payments are due.

To get 10 million in 10 years

• if you want to save $100,000 ($100,000 is the future value) to pay for a project in 10 years, then determine how much you must save each month under conservative guess of fixed interest rate of 8%.

PMT(8%, 10, 0, 100000, 0)

PMT(rate,#per,pv,[fv],[type])

• I am borrowing $10,000 on a 10 month loan with an annual interest rate of 8 percent. What will my monthly payments be? How much principal and interest am I paying each month?

PMT(rate,#per,pv,[fv],[type])

• What would be the monthly payment of a loan with, an annual interest rate of 6%, a 20-year duration, a present value of $150,000 (amount borrowed) and a future value of 0.

RATE(nper, pmt, pv, [fv], [type], [guess])

• If Rate is the only unknown variable, we can use the RATE function to calculate the interest rate.

NPER(rate,pmt,pv,[fv],[type])

• If you can monthly payment $2,074.65 on a 20-year loan, with an annual interest rate of 6%, how long will take to pay off this loan?.

PV(rate, nper, pmt, [fv], [type])

• If we make monthly payments of $1,074.65 on a 20-year loan, with an annual interest rate of 6%, how much can we borrow?

• Future value of an investment based on periodic, constant payments and a constant interest rate.

Rate - The interest rate per period.

Nper - The total number of payment periods in an annuity.

Pmt - The payment(fixed) made each period; Typically, pmt contains principal and interest but no other fees or taxes. If pmt is omitted, you must include the pv argument.

Pv - The present value, or the lump-sum (Down payment) amount that a series of future payments is worth right now. If pv is omitted, it is assumed to be 0 (zero), and you must include the pmt argument.

Type - When payments are due, 0 (end) / 1 (beginning) of the period. If type is omitted, it is assumed to be 0.

FV(rate, #per, [pmt], [pv], [type])

FV(rate,nper,pmt,[pv],[type])

• if we make monthly payments of only $1,000.00, we still have debt after 20 years.

More on Loans

• calculate the monthly payment on a loan with an annual interest rate of 5%, a 2-year duration and a present value (amount borrowed) of $20,000.

PPMT(rate, per, nper, pv, [fv], [type])

• Use the PPMT function to calculate the principal part of the payment.

IPMT(rate, per, nper, pv, [fv], [type])

• Use the IPMT function to calculate the interest part of the payment.

Update the balance.

PPMT(rate, per, nper, pv, [fv], [type])

• Returns the payment on the principal for a given period for an investment based on periodic, constant payments and a constant interest rate.

• Payment on principle for the first month of loan? – loan fraction

IPMT

• Returns the interest payment for a given period for an investment based on periodic, constant payments and a constant interest rate.

• How much interest do I pay for the first month?

• How much interest do I pay for the last year?

IPMT(rate, per, nper, pv, [fv], [type])

• Rate Required. The interest rate per period.• Per Required. The period for which you want to find

the interest and must be in the range 1 to nper.• Nper Required. The total number of payment periods

in an annuity.• Pv Required. The present value, or the lump-sum

amount that a series of future payments is worth right now.

• Fv Optional. The future value, or a cash balance you want to attain after the last payment is made. If fv is omitted, it is assumed to be 0 (the future value of a loan, for example, is 0).

• Type Optional. The number 0 or 1 and indicates when payments are due. If type is omitted, it is assumed to be 0.

ISPMT(rate, per, nper, pv)

• Calculates the interest paid during a specific period of an investment.

• How much interest do I pay during first two year?

CUMIPMT(rate, nper, pv, start_period, end_period, type)

• Returns the cumulative interest paid on a loan between start_period and end_period.

• Ex: Total interest paid in the second year of payments, periods 13 through 24

Asset Depreciation Functions

DB,DDB,SYD,SLN,VBD

SLN(cost, salvage, life)

• The SLN (Straight Line) function is easy. Each year the depreciation value is the same.

SYD(cost, salvage, life, per)

• Returns the sum-of-years' digits depreciation of an asset for a specified period.

• A useful life of 10 years results in a sum of years of 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 55. The asset loses 9000 in value. Depreciation value period 1 = 10/55 * 9000 = 1,636.36. Deprecation value period 2 = 9/55 * 9000 = 1,472,73, etc. If we subtract these values, the asset depreciates from 10,000 to 1000 in 10 years

DB(cost, salvage, life, period, [month])

• Returns the depreciation of an asset for a specified period using the fixed-declining balance method.

DDB(cost, salvage, life, period, [factor])

• Returns the depreciation of an asset for a specified period using the double-declining balance method or some other method you specify.

VDB(cost, salvage, life, start_period, end_period, [factor], [no_switch])

VDB(cost, salvage, life, start_period, end_period, [factor], [no_switch])

• Returns the depreciation of an asset for any period you specify, including partial periods, using the double-declining balance method or some other method you specify. VDB stands for variable declining balance.

• The VDB function performs the same calculations as the DDB function. However, it switches to Straight Line calculation (yellow values) to make sure you reach the salvage value

DB

• Returns the depreciation of an asset for a specified period using the fixed-declining balance method.

• The fixed-declining balance method computes depreciation at a fixed rate.

• DB(cost, salvage, life, period, [month])

DB . .Data Description

1,000,000 Initial cost

100,000 Salvage value

6 Lifetime in years

Formula Description (Result)

=DB(A2,A3,A4,1,7) Depreciation in first year, with only 7 months calculated (186,083.33)

=DB(A2,A3,A4,2,7) Depreciation in second year (259,639.42)

=DB(A2,A3,A4,3,7) Depreciation in third year (176,814.44)

=DB(A2,A3,A4,4,7) Depreciation in fourth year (120,410.64)

=DB(A2,A3,A4,5,7) Depreciation in fifth year (81,999.64)

=DB(A2,A3,A4,6,7) Depreciation in sixth year (55,841.76)

=DB(A2,A3,A4,7,7) Depreciation in seventh year, with only 5 months calculated (15,845.10)

DB(PurchasePrice, SalvageValue, Life, PeriodToCalculate[, FirstYearMonth])

• Calculates deprecation based upon a fixed

percentage.

• To calculates the deprecation monthly basis,

multiplying the years (PeriodToCalculate) by 12.

• If the item was purchased part way through the

financial year, the first years depreciation will be

based on the remaining part of the year.

• Last one is [email protected] 38

DB(PurchasePrice, SalvageValue, Life, PeriodToCalculate[, FirstYearMonth])

[email protected] 39

Investment Value Functions

FV, NPV, PV

FV

• Returns the future value of an investment based on periodic, constant payments and a constant interest rate.

FV(rate, nper, pmt, [pv], [type])

• If I invest $2,000 a year for 40 years toward my retirement and earn 8 percent a year on my investments, how much will I have when I retire? Initially your are paying $3000

FV(rate, nper, pmt, [pv], [type])

Annual interest rate 8% 0.67%

Number of payments 25 300

Amount of the payment 2000 -2000

Present value (lump-sum) 3000 -3000

Payment is due at the beginning (1) of the period 0

$1,924,073.32

FV(rate,#per,[pmt],[pv],[type])NPV

• Should I pay $11,000 today for a copier or $3,000 a year for 5 years?

• net present value of -$10,814.33. (The negative sign means we are paying money out.)

• present value of the payments is $12,112.05, so it's better to pay $11,000 today than to make payments at the beginning of the year.

PV

• Returns the present value of an investment. The present value is the total amount that a series of future payments is worth now.

• For example, when you borrow money, the loan amount is the present value to the lender.

• PV(rate, nper, pmt, [fv], [type])

• Should I pay $11,000 today for a copier or $3,000 a year for 5 years?

PV(rate, nper, pmt, [fv], [type])Rate The interest rate per period.

Nper The total number of payment periods in an annuity.

Pmt The fixed payment made each period over the life of the annuity. If pmt is omitted, you must include the fvargument.

Fv Optional. The future value, or a cash balance you want to attain after the last payment is made. If fv is omitted, it is assumed to be 0 (the future value of a loan, for example, is 0). If fv is omitted, you must include the pmtargument.

Type Optional. 0 (end) / 1 (beginning) of the period.

PV. .Data Description

500 Money paid out of an insurance annuity at the end of every month

8% Interest rate earned on the money paid out

20 Years the money will be paid out


=PV(A3/12, 12*A4, A2, , 0) Present value of an annuity with the terms above (-59,777.15).

NPV(rate,value1,[value2],...)

• Calculates the Net Present Value of an investment by using a discount rate and a series of future payments (negative values) and income (positive values).

NPVData Description

8% Annual discount rate. This might represent the rate of inflation or the interest rate of a competing investment.

-40,000 Initial cost of investment

8,000 Return from first year

9,200 Return from second year

10,000 Return from third year

12,000 Return from fourth year

14,500 Return from fifth year


=NPV(A2, A4:A8)+A3 Net present value of this investment (1,922.06)

=NPV(A2, A4:A8, -9000)+A3 Net present value of this investment, with a loss in the sixth year of 9000 (-3,749.47)


• If I deposit V today (10% FD for 5 years), how much can I get after Y years with compound interest rate of r%.

After Y years = FV ( r%/12, Y*12, V, 0, 0 )

• If I deposit V today and P every month, how much can I get after Y years with fixed interest rate of r%.

After Y years = FV ( r%/12, Y*12, V, P, 0 )


• If a parent deposit 100000 for a their newborn and monthly deposit 5000 for five yearstime. If the interest rate is 10%, what wouldthey get after 25 years?

FV(8%/12,12*20,5000,100000,0)

Internal Rate of Return Functions

IRR,MIRR,XIRR

IRR• Returns the internal rate of return for a series

of cash flows represented by the numbers in values.

• cash flows must occur at regular intervals, such as monthly or annually.

• The IRR is the interest rate received for an investment consisting of payments (negative values) and income (positive values) that occur at regular periods.

IRR(values, [guess])Data Description

-70,000 Initial cost of a business

12,000 Net income for the first year

15,000 Net income for the second year

18,000 Net income for the third year

21,000 Net income for the fourth year

26,000 Net income for the fifth year


=IRR(A2:A6) Investment's internal rate of return after four years (-2%)

=IRR(A2:A7) Internal rate of return after five years (9%)

=IRR(A2:A4,-10%) To calculate the internal rate of return after two years, you need to include a guess (-44%)

MIRR(values, finance_rate, reinvest_rate)

• Values Required. An array or a reference to cells that contain numbers. These numbers represent a series of payments (negative values) and income (positive values) occurring at regular periods.

• Finance_rate Required. The interest rate you pay on the money used in the cash flows.

• Reinvest_rate Required. The interest rate you receive on the cash flows as you reinvest them.

A B

Data Description

-$120,000 Initial cost

39,000 Return first year

30,000 Return second year

21,000 Return third year

37,000 Return fourth year

46,000 Return fifth year

10.00% Annual interest rate for the 120,000 loan

12.00% Annual interest rate for the reinvested profits


=MIRR(A2:A7, A8, A9) Investment's modified rate of return after five years (13%)

=MIRR(A2:A5, A8, A9) Modified rate of return after three years (-5%)

=MIRR(A2:A7, A8, 14%)Five-year modified rate of return based on a reinvest_rate of 14 percent (13%)

Example

• You will receive $15,000 in 5 years time. You are able to borrow and lend at a rate of 4% per year. What is the Present Value of the Investment?

• Answer: PV = $15,000(1.04)-5 = $12,328.91

Example

• You have $12,280.96 in your bank account. You are able to invest the full amount for 5 years, continuously compounded at a rate of 4%. What is the Future Value of the investment?

• Answer: FV = $12,280.96(e0.2) = $15,000

Example

• You are offered the option of choosing between an immediate, one-time, lump sum payment of $12,000, and $1,500 per year for 10 years. You are able to borrow and lend at an annual rate of 4%. Which option should you choose?

• Answer: PV = $1,500[(0.3244)/0.04] = $1,500(8.1108) = $12,166.34. Therefore, you should choose the annuity because it is worth about $166 more in today’s dollars than the lump sum payment.

Problems1. You have won a scholarship. At the end of each of the next 10 years, you'll

receive a payment of $5,000. If the inflation is 10% per year, what's the present value of your scholarship winnings?

2. A perpetuity is an annuity that is received forever. If I rent my house and at the beginning of each year receive $14,000, what is the value of this perpetuity? Assume an annual cost of capital of 10 percent. (Hint: use the PV function and let the number of periods be large!)

3. I now have $250,000 in the bank. At the end of each of the next 20 years, I withdraw $15,000 to live on. If I earn 8 percent per year on my investments, how much money will I have in 20 years?

4. I deposit $1,000 per month (at the end of each month) over the next 10 years. My investments earn 0.8 percent per month. I would like to have $1,000,000 in 10 years. How much money should I deposit now?

5. A player is receiving $15 million at the end of each of the next 7 years. He can earn 6% per year on his investments. What is the present value of his future revenues?

Problems• Use the FV function to determine the value to which $100

accumulates in three years if you are earning 7 percent per year.

• You have a liability of $1,000,000 due in 10 years. The cost of capital is 10 percent per year. What amount of money would you need to set aside at the end of each of the next 10 years to meet this liability?

• I currently have $10,000 in the bank. At the beginning of each of the next 20 years, I am going to invest $4,000, and I expect to earn 6 percent per year on my investments. How much money will I have in 20 years?

Problems• At the end of each of the next 20 years, I will receive the following

amounts:

• Use the PV function to find the present value of these cash flows if the cost of capital is 10 percent. Hint: Begin by computing the value of receiving $400 a year for 20 years, and then subtract the value of receiving $100 a year for 10 years, and so on.

• We are borrowing $200,000 on a 30-year mortgage with an annual interest rate of 10 percent. Assuming end of month payments, determine the monthly payment, interest payment each month, and amount paid toward principal each month.

Years Amounts

1-5 $200

6-10 $300

11-20 $400

Problems• You are going to buy a new car. The cost of the car is $50,000. You have been

offered two payment plans:

– A 10 percent discount on the cost of the car, followed by 60 monthly payments financed at 9 percent per year.

– No discount on the cost of the car, but the 60 monthly payments are financed at only 2 percent per year.

If you believe your annual cost of capital is 9 percent, which payment plan is a better deal? Assume all payments occur at the end of the month.

• A balloon mortgage requires you to pay off part of a loan during a specified time period, and then make a lump sum payment to pay off the remaining portion of the loan. Suppose you borrow $400,000 on a 20-year balloon mortgage and the interest rate is .5 percent per month. Your end of month payments during the first 20 years are required to pay off $300,000 of your loan, and 20 years from now you will have to pay off the remaining $100,000. Determine your monthly payments for this loan.

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