onsider the following two mutually exclusive projects: (a)What is the payback pe

Question

onsider the following two mutually exclusive projects:

(a)What is the payback period for Project A?

(b) What is the payback period for Project B?

(c) What is the discounted payback period for Project A?

(d) What is the discounted payback period for Project B?

(e) What is the NPV for Project A?

(f) What is the NPV for Project B ?

(g) What is the IRR for Project A?

(h) What is the IRR for Project B?
(i) What is the profitability index for Project A?

Year Cash Flow (A) Cash Flow (B) 0 –$259,169        –$16,532          1 25,400        5,896          2 58,000        8,869          3 53,000        13,980          4 393,000        8,281         

Explanation / Answer

Computation of Payback period

Years Project A Cummulative cash flows Project B Cummulative cash flows

1 25400 25400 5896 5896

2 58000 83400 8869 14765

3 53000 136400 13980 28745

4 393000 529400 8281 37026

a. Payback period of Project A:

= 3 years + 122769 / 393000

= 3 + 0.31

= 3.31.

b. Payback period of Project B

= 2 years + 1767 / 13980

= 2+ 0.13 = 2.13

Computation of Discounted pay back period

Years Project A Discount@ 6% PV cash flows CCF Project B PV cash flows CCF

1 25400 0.943 23952 23952 5896 5560 5560

2 58000 0.890 51620 75572 8869 7893 13453

3 53000 0.839 44467 120039 13980 11729 25182

4 393000 0.792 311256 431295 8281 6559 31741

c. Discounted pay back period of project A

= 3 years + 139130 / 311256

= 3 years + 0.45

= 3.45

d. Discounted Payback period of Project B

= 2 years + 3079 / 11729

= 2 years + 0.26

= 2.26

Years Project A Discount@6% PV cash inflows Project B PV cash inflows

1 25400 0.943 23952 5896 5560

2 58000 0.890 51620 8869 7893

3 53000 0.839 44467 13980 11729

4 393000 0.792 311256 8281 6559

total cash inflows 431295 31741

less initial investment (259169) (16532)

NPV 172126 15209

e. NPV of Project A is$ 172126

f. NpV of project B is $15209

Computation of IRR of Project A and Project B

Years Project A Discount@ 6% PVCF discount@10% PVCF Project B PVCF @6% PVCF@10%

1 25400 0.943 23952 0.909 23089 5896 5560 5359

2 58000 0.890 51620 0.826 47908 8869 7893 7326

3 53000 0.839 44467 0.751 39803 13980 11729 10499

4 393000 0.792 311256 0.683 268419 8281 6559 5656

total cash inflows 431295 379219 31741 28840

less: initial investment (259169) (259169) (16532) (16532)

NPV 172126 120050 15209 12308

IRR = lower rate + NPV lower rate / (NPV lower rate - NPV higher rate) * difference factor

g. IRR of Project A

IRR = 6+ 172126 / (172126 - 120050 ) * 4

= 19%

h. IRR of Project B

IRR = 6 + 15209 / (15209 - 12308) * 4

= 27%

Profitatability index = present value of cash inflows / present value of cash out flows

i. Profitablity inder of Project A

profitability index = 431295 / 259169 = 1.66

j. Profitability index of Project B

profitability index = 31741 / 16532 = 1.92.

  

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