Corporate Finance Chapter 10 - Even Solutions
(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:
Year Truck Pulley
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 +
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:
Year Truck Pulley
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 +