Corporate Finance Chapter 10 - Even Solutions

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(10-2) IRR
A project has an initial cost of $52,125, expected net cash inflows of $12,000 per year for 8 years, and a cost of capital of 12%. What is the project’s NPV? (Hint: Begin by constructing a time line.) What’s the project’s IRR? NPV = Cash Flow in Period n/ (1 + Discount Rate)n

NPV = $52,125 + 12,000/(1 +.12)8 = 4,846.60
12,000/(1 +.12)7 = 5,428.19
12,000/(1 +.12)6 = 6,079.58
12,000/(1 +.12)5 = 6,809.13
12,000/(1 +.12)4 = 7,626.21
12,000/(1 +.12)3 = 8,541.35
12,000/(1 +.12)2 = 9,566.33
12,000/(1 +.12)1 = 10,714.29
-52,125
Add each NPV to get NPV = $7,486.68
IRR in excel – CF0 = -52,125, CF1-8= 12,000, IRR = 16%

(10-4) Profitability Index
Refer to previous problem. What the project’s profitability index? PI = 1 + NPV/Investment Required = 1 + $7,486.68/$52,125 = PI = 1.14

(10-6) What is the project’s discounted payback period?
Year 6 = $-2,788.11, Year 7 = $+2,640.08, so between year 6-7 2,788.11/5,428.19 = .514 = 6.51 years

(10-8) NPVs, IRRs, and MIRRs for Independent Projects
Edelman Engineering is considering including two pieces of equipment, a truck and an overhead pulley system, in this year’s capital budget. The projects are independent. The cash outlay for the truck is $17,100 and that for the pulley system is $22,430. The firm’s cost of capital is 14%. After-tax cash flows, including depreciation, are as follows:

YearTruckPulley
1$5,100$7,500
2$5,100$7,500
3$5,100$7,500
4$5,100$7,500
5$5,100$7,500

Calculate the IRR, the NPV, and the MIRR for each project, and indicate the correct accept–reject decision for each. TRUCK -
-17,100 + 5,100/(1+.14)1 + 5,100/(1+.14)2 + 5,100/(1+.14)3 + 5,100/(1+.14)4 + 5,100/(1+.14)5 = -17,100 + 4,473.68421 + 3,924.2844 + 3,442.36403 + 3,019.6097 + 2,648.78649 = $408.73 In excel with same cash flows as above, IRR = 15%

MIRR – using same cash flows as values and .14 as reinvestment rate, MIRR = 14.54% Accept.
PULLEY –
-22,430 + 7,500/(1+.14)1 + 7,500/(1+.14)2 + 7,500/(1+.14)3 + 7,500/(1+.14)4 + 7,500/(1+.14)5 = -22,430 + 6,578.94737 + 5,771.00646 + 5,062.30004 + 4,440.60250 + 3,895.27425 = $3,318.13 In excel, using same cash flows as above, IRR = 20%

In excel, using cash flows as values and .14 as reinvestment rate, MIRR = 17.19% Accept.

(10-10) Capital Budgeting Methods
Project S has a cost of $10,000 and is expected to produce benefits (cash flows) of $3,000 per year for 5 years. Project L costs $25,000 and is expected to produce cash flows of $7,400 per year for 5 years. Calculate the two projects’ NPVs, IRRs, MIRRs, and PIs, assuming a cost of capital of 12%. Which project would be selected, assuming they are mutually exclusive, using each ranking method? Which should actually be selected? Project S

NPV = -10,000 + 3,000 (1+.12)1 + 3,000 (1+.12)2 + 3,000 (1+.12)3 + 3,000 (1+.12)4 + 3,000 (1+.12)5 = -10,000 + 2,678.57143 + 2,135.3377 + 1,736.11111 + 1,906.55346 + 1,702.28219 = NPVs = $814.33 IRRs in excel = 15.24%

MIRRs in excel = 13.77%
PI = 1 + NPV/Investment Required = 1+ 814.33/10,000 = PI = 1.081 Project L
NPV = -25,000 + 7,400 (1+.12)1 + 7,400(1+.12)2 + 7,400 (1+.12)3 + 7,400 (1+.12)4 + 7,400 (1+.12)5 = -25,000 + 6,607.14286 + 5,899.23469 + 5,267.16634 + 4,702.83187 + 4,198.96274 = NPVL = $1,675.34 IRRL in excel = 14.67%

MIRRL in excel = 13.46%
PI = NPV/Investment Required = 1+ 1,675.34/25,000 = PI = 1.067 Using the NPV comparison, Project L appears to be the better investment. The IRR and MIRR are very close but make Project S appear to be the better investment. Using the Predictability Index, Project S appears to be more of a “bang for the buck”.

(10-12) NPV and IRR Analysis
After discovering a new gold vein in the Colorado mountains, CTC Mining Corporation must decide whether to go ahead and develop the deposit. The most cost-effective method of mining gold is sulfuric acid extraction, a process that could result in environmental damage. Before proceeding with the extraction, CTC must spend...
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