Question

Fincher Manufacturing (FM) is considering two mutually exclusive capital investments to
utilize an idle factory owned by the firm. The first alternative calls for manufacturing tundratorque drill bits required for the extraction of rare earth metals from the frozen tundra of
Greenland. This proposal would generate after-tax cash inflows of $12 million per year
beginning in one year (at date 1). Due to the current scarcity of rare earth metals, the yearly
cash flows for this project are expected to grow by 5 percent per year in perpetuity from date
1 on. The second alternative calls for producing the Polycrystalline Diamond Compact bits
frequently used in horizontal drilling operations. Alternative two will generate constant
yearly after-tax cash flows of $20 million beginning in one year (at date 1) and remaining
constant in perpetuity. Assuming each project requires an initial investment of $120 million:
a. Which capital investment project has the greater IRR?

b. Which project has a greater NPV if Fincher’s cost of capital is 10 percent.

c. Determine the range of estimates for Fincher’s cost of capital for which investing in the
project having the greater IRR maximizes the value of the firm.

Answer 1

a) Using dividend growth model, IRR (Rare earth) = CF / P + g = 12 / 120 + 5% = 15.0%

IRR (Diamond) = CF / P = 20 / 120 = 16.67%

b) NPV (rare earth) = CF / (r - g) - P = 12 / (10% - 5%) - 120 = $120 million

NPV (Diamond) = CF / r - P = 20 / 10% - 120 = $80 million

r	NPV 1	NPV 2
6%	$        1,080	$              213
7%	$            480	$              166
8%	$            280	$              130
9%	$            180	$              102
10%	$            120	$                 80
11%	$              80	$                 62
12%	$              51	$                 47
13%	$              30	$                 34
14%	$              13	$                 23
15%	$               -	$                 13
16%	$            (11)	$                   5
17%	$            (20)	$                 (2)
18%	$            (28)	$                 (9)
19%	$            (34)	$               (15)

For IRR below 13%, choose the rare earth project, else the diamond project.