Question

Three mutually exclusive investment alternatives are being considered. The estimated cash flows for each alternative are given below. The study period is 30 years and the​ firm's MARR is 17% per year. Assume repeatability and reinvestment of positive cash balances at 17​% per year.

a. What is the simple payback period for Alternative​ 1?

b. What is the annual worth of Alternative​ 2?

c. What is the IRR of the incremental cash flows of Alternative 2 compared to Alternative​ 1?

d. Which alternative should be selected​?

                                                                 Alt. 1               Alt. 2      Alt. 3

Capital Investment                                   -25,000   -60,000 -45,000

Annual Costs                                                 -12,000 -30,000 -20,000

Annual Revenues                                           28,000 57,500 38,000

Market Value at End of Useful Life            9,000     9,000     9,000

Useful Life, years                                          5               5              6

IRR                                                        59.9%                37.7%    34.4%

Answer 1

Calculation of Net Annual Cash Flow:

Particular	Alternative1	Alternative2	Alternative3
Annual Revenue	28000	57500	38000
Annual Cost	12000	30000	20000
Net Cash Flow	16000	27500	18000

(a)

Calculation of Payback Period(PBP):

Payback period is the period in which the Cost of a project is recovered from the revenues of the projects.

Formula:Payback period(in case of equal cash flows)=Cost of a project/Annual Cash Flows

PBP(Alternative1)=25000/16000

=1.5625 Years or 1year 7months approx

(b) Calculation of Annual worth of  Alternative2:

Annual worth is the equivalent annual net cash flow of the cash flows to be received throughout the life of a project.

IRR is the annual rate of return of the cash flows of a project. In other words IRR is the rate which if used for discounting the cash flows, equates the net cash flows(including scrap) to the intial investment or the cost of the project.

We know that

Present value of cash flows=Annual Cash flows*PV factor of annuity @ r rate for n periods

PV factor of annuity= [(1+r)^{^n}-1] / [(1+r)^{^n}*r]

PV factor of annuity for 37.7% for 5 years=[(1+.377)^{^5}-1] / [(1+.377)^{^5}*.377]

=2.116737

Again

Present value of cash flows=Annual Cash flows*PV factor of annuity @ r rate for n periods

60000=Annual Cash flows*2.116737

Annual Cash flows=60000/2.116737

=28345.5

(c) Calculation of incremental Cash flows:

Particular	Alternative1	Alternative2	Incremental(Alt2-Alt1)
Annual Revenue	28000	57500	29500
Annual Cost	12000	30000	18000
Net Cash Flow	16000	27500	11500
Cost of Project	25000	60000	35000

Incremental Cost=Incremental Net Cash Flows*PV factor of annuity at r rate for 5 years

35000=11500*PV factor of annuity

PV factor of annuity=35000/11500

=3.0435

Look 3.0435 in the 5th year's column in the PV of annuity table. 3.0576(which is nearly equal to 3.0435) is before 19% rate hence IRR should be between 19% to 20%.

We can find exact IRR by using IRR functin of excel:

Year	Cash Flow
0	-35000
1	11500
2	11500
3	11500
4	11500
5	11500
IRR	19.21%

Formula: =IRR(B2:B7)

We could find Exact IRR without using excel as well by using following formula:

Hence the result is same as we calculated using excel.

Note: NPV for both the rates have been calculated by discounting the incremental cash flows(i.e.11500) by repective rates and deducting Incremental Cost of investments from the Present Value of Cash flows.

(D)

Project A has highest IRR(59.9%) hence Project A should be selected.

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