Question

3. Considering the following two mutually exclusive projects: Year Cash Flow (A) 0 -$750,000 1 105,000 2 175,000 3 250,000 4 545,000 Cash Flow (B) -$75,000 70,000 15,000 10,000 2,000 Whichever project you choose, if any, you require a 9 percent return on your investment. a. If you apply the payback criterion, which investment will you choose? Why? b. If you apply the discounted payback criterion, which investment will you choose? Why? c. If you apply the NPV criterion, which investment will you choose? Why? d. If you apply the IRR criterion, which investment will you choose? Why? e. If you apply the profitability index criterion, which investment will you choose? Why? f. Based on your answers in (a) through (e), which project will you finally choose? Why? g. Calculate the crossover rate. Why is there a conflict between project A and project B (explain in terms of crossover rate)?

Answer 1

a.

The investment remaining in year 0 is the initial investment, and adding the cash flow received that year will give the investment remaining for that year. Once the investment remaining becomes positive, the payback period is complete.

The payback period for Project A is after 3 years while for Project B is after 1 year. Project B will be selected on the basis of payback period.

b.

To find the discounted payback period, we use the same method as before except we use the discounted cashflows, discounted by 9%.

Again, the payback period for Project A is after 3 years while for Project B is after 1 year. Project B will be selected on the basis of payback period.

c.

NPV is the sum of the discounted cashflows minus the initial investment.

As seen in the above table, the last cell in the 'Investment Remaining' row will give the NPV

NPV of Project A is $72,761.88 and that of project B is $10,984.07. Since project A has a greater NPV, it should be selected

d.

IRR is the rate of return for which the NPV will be 0

Using the IRR function, the IRR for project A is 12.37% and for project B is 20.6%. Based on IRR, projecct B should be selected.

e.

Profitability Index = PV of future cashflows / Initial investment

(PV of future cashflows are the discounted cashflows used in the second table)

For project A,

Profitability index = (96,330.28 + 147,294 + 193,045.87 + 386,091.74) / 750,000 =  822,761.88 / 750,000 = 1.10

For project B.

Profitablitiy index = (64,220.18 + 12,625.2 + 7,721.83 + 1,416.85) / 75,000 = 1.15

Based on profitability index, project B should be selected.

f.

Crossover rate is the rate at which the NPV of both projects will be the same.

Let r be the crossover rate

NPV_A = -750,000 + 105,000 / (1 + r) + 175,000 / (1 + r)² + 250,000 / (1 + r)³ + 545,000 / (1 + r)⁴

NPV _B = -75,000 + 70,000 / (1 + r) + 15,000 / (1 + r)² + 10,000 / (1 + r)³ + 2,000 / (1 + r)⁴

NPV_A = NPV_B

-750,000 + 105,000 / (1 + r) + 175,000 / (1 + r)² + 250,000 / (1 + r)³ + 545,000 / (1 + r)⁴ = -75,000 + 70,000 / (1 + r) + 15,000 / (1 + r)² + 10,000 / (1 + r)³ + 2,000 / (1 + r)⁴

-675,000 + 35,000 / (1 + r) + 160,000 / (1 + r)² + 240,000 / (1 + r)³ + 543,000 / (1 + r)⁴ = 0

Using trial and error or IRR function in excel for above cashflows, r = 11.99%

e.

Since the NPV in project A is higher, it will increase the overall value of the firm, so it should be selected.

g. The majority of cashflows in Project A are at the end of the project while for Project B they are at the beginning. That is why the payback periods are lower for project B than for project A. The higher crossover rate will have more effect on the higher, later cashflows of Project A than they will for the higher, earlier cashflows of project B, and reduces the NPV of project A more than it does for Project B.