Question

Hollow Truth Publishers is considering whether to launch a new e-magazine. The annual percentage rate of return (APR) on a similar risk project is 8%, the cash flows occur semi-annually (at the end of the 6th and 12th month for each year), and the publishing company requires a payback period of 2 years. The finance department has calculated that the required rate of return for all projects that it will consider is 14%.

The costs of the project are:

Advertising on various billboards and cable television stations $200,000

Hollow Truth’s headquarters accounting department charges $50,000

Production costs and employee bonuses $260,000

Last year’s purchase price for the e-magazine's offices $470,000

Potential rental income from the offices if rented to a 3rd party $200,000

a. What are the total relevant costs of the project? Explain why you consider each cost relevant or not for this project.
b. Assume the semi-annual cash inflows are $150,000 and $200,000 in year 1, and $250,000 and $200,000 in year 2. Calculate the payback, discounted payback, IRR and MIRR of the project. Based on each criterion, should you accept the project? Why?
c. If the project is analyzed using the NPV rule, should you accept the project? Why?
What would you do if you believed the semi-annual cash flows had a high degree of uncertainty and could be potentially 15% lower? (You don’t have to re-estimate the NPV, just describe what you would do and how you would assess this.)
d. If you were the CEO of the firm, would you accept or reject this project? Why?   

Answer 1

a) What are the total relevant costs of the project? Explain why you consider each cost relevant or not for this project.

Advertising = $200,000

Production costs = $260,000

Potential rents = $200,000

Total = $660,000

The accounting department charges are allocated overhead and last year's purchase price is a sunk cost so it will not be included.

b)  Assume the semi-annual cash inflows are $150,000 and $200,000 in year 1, and $250,000 and $200,000 in year 2. Calculate the payback, discounted payback, IRR, and MIRR of the project. Based on each criterion, should you accept the project? Why?

-The accumulated cash flows at the end of the third period are $600,000 and $800,000 at the end of the fourth period. Payback for the project will occur between the third and fourth cash flows (the first and last cash flow in year 2).

Total costs are $660,000

Payback = 1.5 yrs+[(660,000–600,000)/200,000]*0.5 yrs = 1.65years

Accept because it is paid back in the pre-specified period, 2 years.

The discounted accumulated cash flows at the end of the third period are $551,391 and $722,352 at the end of the fourth period. Discounted Payback for the project will occur between the third and fourth cash flows (the first and last cash flow in year 2).

Total costs are $660,000

Payback = 1.5 yrs+[(660,000–551,391)/170,961]*0.5 yrs = 1.82 years

Accept because it is paid back in the pre-specified period, 2 years.

IRR is that r which makes the NPV equal to 0. Remember IRR is solved by iteration. If you are doing IRR by hand, you need to use trial and error to find IRR. Alternatively, your financial calculator probably has an IRR function and Excel has an IRR function. Since these cash flows are semi-annual, the computed r is semi-annual. So the annual IRR is 16.06% ((1.0773^2)–1).

0 =-$660,000 + (150,000)/(1+IRR)^1+ (200,000)/(1+IRR)^2+ (250,000)/(1+IRR)^3+(200,000)/(1+IRR)^4

Solve for IRR, IRR=0.0773

Since the finance department requires a 14% return, you would accept this project (16.06%>14%)

Since the IRR is 16% while the appropriate r is only 8%, IRR overstates the expected return due to the reinvestment rate assumption. In other words, IRR assumes that all the intermediate cash flows are reinvested at 16%. MIRR solves that problem by assuming that the intermediate cash flows are reinvested at an r that is closer to the appropriate r which is 8%. The semi-annual MIRR is 6.37% while the annual rate is 13.15% ((1.0637^2)-1).

PV(outflows) =-660,000 (in period 0 dollars)

FV(inflows, period 4 dollars) = 150,000*(1.04^3) + 200,000*(1.04^2) + 250,000*(1.04^1) + 200,000*(1.04^0)

= 845,050

MIRR = {[FV/PV] ^ (1/T)}-1 = {[845,050/660,000] ^ (1/4)}–1 = 0.0637

Since the finance department requires a 14% return, you would reject this project (13.15%<14%)

c. If the project is analyzed using the NPV rule, should you accept the project? Why?
What would you do if you believed the semi-annual cash flows had a high degree of uncertainty and could be potentially 15% lower? (You don’t have to re-estimate the NPV, just describe what you would do and how you would assess this.)

semi-annual rate = .04

NPV = -$660,000 + (150,000)/(1.04)^1+ (200,000)/(1.04)^2+ (250,000)/(1.04)^3+(200,000)/(1.04)^4

NPV = $62,352

Therefore, accept the project because NPV > 0

If there is a high degree of uncertainty about the semi-annual cash flows the first question that needs to be addressed is did you pick the correct r. In this case, assume you have the correct r and instead the uncertainty comes from whether you have the correct estimated cash flows. In that case, we should do a scenario analysis that includes assigning probabilities to each cash flow outcome and re-estimate NPV.

d. If you were the CEO of the firm, would you accept or reject this project? Why?

All of the other methods have various advantages and disadvantages but in the end, you want to focus on NPV because it is the only method that always is consistent with maximizing shareholder wealth. Therefore you want to accept this project because the NPV>0. Note that IRR and MIRR should be consistent with NPV in this case because the cash flows are conventional and the project is independent. However, the finance department has established a hurdle rate (14%) that does not reflect the riskiness of the cash flows so these two methods may lead to sub-optimal decisions

If you have any doubts please let me know in the comments.

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