METHODS OF EVALUATING CAPITAL INVESTMENTS

I. Non-discounted cash flow techniques:

A. Payback period (payoff/payout period) – measures the length of time required to recover the initial investment

Decision rule: Accept if payback < required maximum payback Reject if payback > required maximum payback

1. Even cash flowsPayback Period = Net Investment

Annual CFAT2. Uneven cash flows

Payback Period = point where the cumulative cash flows equal the net investment

Example 1:

Initial Investment P 1,000,000 Annual operating CFAT P 300,000 Economic life 8 years

Payback Period = P1,000,000 ÷ P300,000 = 3.33 years or 3 yrs. & 4 mos. ======== ===========

Example 2:

Initial Investment P1,000,000 CFAT:

Year 1 150,000 2 200,000

3 250,0004 300,0005 400,0006 350,0007 150,0008 100,000

Payback Period:

Cumulative Year CFAT CFAT 1 150,000 150,000 2 200,000 350,000 3 250,000 600,000 4 300,000 900,000 ) Payback = 4.25 yrs. 5 400,000 1,300,000 ) ======

1

Advantages:

easy to compute and understand used to measure degree of risk associated with a project generally, the longer the payback period, the higher the risk used to select projects which provide a quick return of invested funds

Disadvantages:

ignores the time value of money the cutoff payback is a subjectively determined number ignores cash inflows after the payback period does not distinguish between projects with different lives conventional payback fails to consider salvage value, if any does not measure profitability, only liquidity of the project

B. Payback reciprocal – determines the portion or percentage of the net investment that is recovered in one year.

1 or Ave. Free Cash Flows = Payback period Net Investment

- a project with an infinite life would have an IRR equal to its payback reciprocal.

- when a project’s life is at least twice the payback period and the annual free cash flows are approximately equal, the payback reciprocal may be used to estimate the IRR

C. Payback bailout period – measures the length of time where the accumulated annual free cash inflows and the salvage value for the period is, at least equal to the net investment.

Example 3:

Initial Investment P 2,000,000Economic life 8 yearsAnnual CFAT P 600,000Salvage value: P 700,000 at the end of Yr. 1 and

will decline at the rate of P100,000 annually

Compute the payback bailout period.

2

Cumulative Salvage Total PaybackYear CFAT CFAT + Value = CFAT Bailout 1 600,000 600,000 700,000 1,300,000 1 2 600,000 1,200,000 600,000 1,800,000 1 3 600,000 1,800,000 500,000 2,300,000 .5

2.5 yrs

Since Yr. 3 cumulative cash inflow of P 2,300,000 is greater than the net investment of P 2,000,000, payback bailout for Year 3 is computed using the following formula:

= Net Investment – (Cumulative CFAT last year + Salvage value this year)CFAT this year

= P2,000,000 – ( P1,200,000 + P500,000 ) = .5 years P600,000 ======

D. Accounting rate of return (also called the book value method, unadjusted rate of return method, simple rate of return method, or return on investment method)

- measures the rate of return on the net investment (based on net income)

Decision rule: Accept if ARR > required rate of return Reject if ARR < required rate of return

1. Based on initial investment

= Average Annual Net Income After Tax Initial or Net Investment

2. Based on average investment

= Average Annual Net Income After Tax Net Investment + Salvage Value

2Example 4:

Initial investment P 800,000Salvage value 60,000Life 5 yearsAnnual net income after tax:

Year 1 P 100,0002 150,0003 300,0004 200,0005 350,000

Compute for the accounting rate of return based on (a) initial investment and (b) average investment

3

(a) P1,100,000 ÷ 5 = 27.50% P800,000 =====

(b) P1,100,000 ÷ 5 --------------------------------- = 51.16% P800,000 + P60,000 ===== ------------------------- 2

Advantages: easily understood used as a rough preliminary screening device of investment proposals

Disadvantages: ignores the time value of money ignores the timing component of cash inflows averaging may yield inaccurate answers utilizes concepts of capital and net income primarily designed for the purpose

of financial statement preparation and may not be relevant for the evaluation of investment proposals

II. Discounted cash flow techniques:

A. Net present value (NPV) – the excess of the present value of cash inflows over the present value of the net investment.

Present value of cash flows + Terminal cash flows Less: Net InvestmentNet Present Value

Decision rule: Accept if NPV > 0 Reject if NPV < 0

B. Present value index (profitability/desirability index or benefit-cost ratio)

- ratio of the present value of cash inflows to the present value of the net investment

- useful in evaluating projects of different sizes

Present value of free cash flows + Terminal cash flows Divided by: Net InvestmentPresent Value Index

Decision rule: Accept if PVI > 1 Reject if PVI < 1

C. Present value/discounted payback – measures the length of time to recover the net investment, while at the same time, earning the desired rate of return

4

- same procedure as computing for payback period when cash flows are uneven, but using the present value of the cash flows

D. Internal rate of return (IRR) – also called discounted rate of return, time-adjusted rate of return, investor’s method

- the rate that equates the present value of cash inflows to the net investment

For even cash flows:1. Compute the payback period 2. Refer to PVIFA table for the factor closest to answer obtained in step 1.3. Interpolate, if necessary

For uneven cash flows:1. Compute the payback period using the average cash flows2. Refer to PVIFA table for the factor closest to the answer obtained in step 1. THIS

MAY NOT BE THE IRR. Use this “trial rate” as a starting point only for trial and error.

3. Compute the NPV using the “trial rate”. You get the IRR if NPV = 0.4. If NPV obtained using a “trial rate” is > 0, the rate is too low, and a higher rate

should be tried5. If NPV obtained using a “trial rate” is < 0, the rate is too high, and a lower rate

should be tried6. Interpolate (between a positive and a negative NPV) to get the exact IRR

Decision rule: Accept if IRR > Required rate of return Reject if IRR < Required rate of return

E. Annualized net present value (ANPV) or Equivalent Annual Annuity (EAA) – an approach in evaluating projects with unequal lives; converts the net present value of unequal-lived, mutually exclusive projects into an equivalent annual amount (in NPV terms)

Decision rule: Select the project with the highest ANPV

Net Present ValueDivided by: PVIFA factor

Annualized net present value

F. Replacement Chain – used in ranking projects with unequal lives; equalizes the life spans of the projects then comparing the NPVs.

G. Modified internal rate of return (MIRR) – a variation of the IRR; used to eliminate the reinvestment rate assumption of the IRR; useful in ranking projects with time disparity.

- the discount rate that equates the PV of the cash outflows with the PV of the terminal value

Decision rule: Accept if MIRR > Required rate of return Reject if MIRR <Required rate of return

5