Question

1. Decision Rules. Suppose your firm is choosing between two new product lines. One project has an initial investment of $450 million and offers annual cashflows of $160 million for 5 years. The other has an initial investment of $1,560 million and offers annual cashflows of $475 million for 5 years.
   1. Using the payback period, which project would you suggest? (2 points)
   2. If your cost of capital is estimated to be 7%, which project offers the higher NPV? (4 points)
   3. What is the IRR of each project? If you used the IRR, which project would you select? (4 points)
   4. What is the cross-over rate for these projects? Which project is preferred below that rate? Which project is preferred above that rate? (10 points)
   5. Plot the NPV profile for these projects. (Hint: use the NPV at 7%, the crossover rate, and the IRRs) (5 points)

Answer 1

From the graph below we can see that the cross over rate is 13%. Above 13% Project 1 will be preferred and below 13% Project 2 will be preferred.

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Answer 2

Using the payback period method:

• The first project has a payback period of $450 million/$160 million per year = 2.81 years

• The second project has a payback period of $1,560 million/$475 million per year = 3.28 years

Therefore, based on the payback period method, the first project is preferred.

Using the net present value (NPV) method:

• For the first project, the present value of cashflows is: PV = -$450 million + $160 million*(1-1/(1+0.07)^5)/0.07 = $282.49 million

• For the second project, the present value of cashflows is: PV = -$1,560 million + $475 million*(1-1/(1+0.07)^5)/0.07 = $626.95 million

Therefore, based on the NPV method, the second project is preferred.

Using the internal rate of return (IRR) method:

• For the first project, the IRR is 18.23%

• For the second project, the IRR is 15.56%

Therefore, based on the IRR method, the first project is preferred.

The crossover rate is the rate at which the NPVs of the two projects are equal. To find the crossover rate, we can set the present values of the two projects equal to each other and solve for the interest rate:

-$450 million + $160 million*(1-1/(1+r)^5)/r = -$1,560 million + $475 million*(1-1/(1+r)^5)/r

Solving this equation gives a crossover rate of approximately 11.63%.

• Below the crossover rate of 11.63%, the first project is preferred

• Above the crossover rate of 11.63%, the second project is preferred

To plot the NPV profile, we can calculate the NPV for various discount rates and plot them on a graph:

Discount rate	Project 1 NPV	Project 2 NPV
0%	$110 million	$235 million
5%	$159 million	$368 million
7%	$282 million	$627 million
10%	$502 million	$1,009 million
15%	$980 million	$2,076 million

Based on the NPV profile, we can see that the NPV of project 2 is higher than the NPV of project 1 for discount rates above the crossover rate, which confirms our previous findings.