Chapter 8 Finance
Consider the following cash flows: Year Cash Flow 0 −$31,000 1 17,300 2 15,200 3 10,600 Requirement 1: What is the profitability index for the above set of cash flows if the relevant discount rate is 10 percent? Requirement 2: What is the profitability index if the discount rate is 15 percent? Requirement 3: What is the profitability index if the discount rate is 22 percent?
CFo $0 C01 $17,300 F01 1 C02 $15,200 F02 1 C03 $10,600 F03 1 same flow sheets I = 10 NPV CPT $36,253.19 @10%: PI = $36,253.19 / $31,000 = 1.169 I = 15 NPV CPT $33,506.53 @15%: PI = $33,506.53 / $31,000 = 1.081 I = 22 NPV CPT $30,230.13 @22%: PI = $30,230.13 / $31,000 = .975
For the given cash flows, suppose the firm uses the NPV decision rule. Year Cash Flow 0 -$ 153,000 1 78,000 2 67,000 3 49,000 Requirement 1: At a required return of 9 percent, what is the NPV of the project? Requirement 2: At a required return of 21 percent, what is the NPV of the project?
Calculator Solution: CFo -$153,000 C01 $78,000 F01 1 C02 $67,000 F02 1 C03 $49,000 F03 1 use same top but different bottom I = 9% I = 21% NPV CPT NPV CPT $12,789.18 -$15,116.07
Consider the following cash flows: Year Cash Flow 0 -$ 27,000 1 11,400 2 16,300 3 9,400 Required: What is the IRR of the above set of cash flows? (
Calculator solution: CFo -$27,000 C01 $11,400 F01 1 C02 $16,300 F02 1 C03 $9,400 F03 1 IRR CPT 18.21%
You're trying to determine whether or not to expand your business by building a new manufacturing plant. The plant has an installation cost of $14 million, which will be depreciated straight-line to zero over its four-year life. Required: If the plant has projected net income of $1,253,000, $1,935,000, $1,738,000, and $1,310,000 over these four years, what is the project's average accounting return (AAR)?
Our definition of AAR is the average net income divided by the average book value. The average net income for this project is: Average net income = ($1,253,000 + 1,935,000 + 1,738,000 + 1,310,000) / 4 Average net income = $1,559,000 And the average book value is: Average book value = ($14,000,000 + 0) / 2 Average book value = $7,000,000 So, the AAR for this project is: AAR = Average net income / Average book value AAR = $1,559,000 / $7,000,000 AAR = .2227, or 22.27%
A firm evaluates all of its projects by applying the IRR rule. Year Cash Flow 0 -$ 153,000 1 78,000 2 67,000 3 49,000 Requirement 1: What is the project's IRR?
Since the cash flows are conventional and the IRR is greater than the required return, we would accept the project. Calculator Solution: CFo -$153,000 C01 $78,000 F01 1 C02 $67,000 F02 1 C03 $49,000 F03 1 IRR CPT 14.02%
Chamberlain Corp. is evaluating a project with the following cash flows: Year Cash Flow 0 -$ 19,500 1 7,930 2 9,490 3 8,970 4 7,210 5 - 3,980 Required: The company uses an interest rate of 10 percent on all of its projects. Calculate the MIRR of the project using all three methods.
The MIRR for the project with all three approaches is: Discounting approach: In the discounting approach, we find the value of all cash outflows at time 0, while any cash inflows remain at the time at which they occur. So, discounting the cash outflows at time 0, we find: Time 0 cash flow = -$19,500 - $3,980 / 1.105 Time 0 cash flow = -$21,971.27 So, the MIRR using the discounting approach is: 0 = -$21,971.27 + $7,930 / (1 + MIRR) + $9,490 / (1 + MIRR)2 + $8,970 / (1 + MIRR)3 + $7,210 / (1 + MIRR)4 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: MIRR = 19.75% Reinvestment approach: In the reinvestment approach, we find the future value of all cash except the initial cash flow at the end of the project. So, reinvesting the cash flows to Time 5, we find: Time 5 cash flow = $7,930(1.104) + $9,490(1.103) + $8,970(1.102) + $7,210(1.10) - $3,980 Time 5 cash flow = $39,046.20 So, the MIRR using the reinvestment approach is: 0 = -$19,500 + $39,046.20/(1+MIRR)5 $39,046.20 / $19,500 = (1+MIRR)5 MIRR = ($39,046.20 / $19,500)1/5 - 1 MIRR = .1490, or 14.90% Combination approach: In the combination approach, we find the value of all cash outflows at Time 0, and the value of all cash inflows at the end of the project. So, the value of the cash flows is: Time 0 cash flow = -$19,500 - $3,980 / 1.105 Time 0 cash flow = -$21,971.27 Time 5 cash flow = $7,930(1.104) + $9,490(1.103) + $8,970(1.102) + $7,210(1.10) Time 5 cash flow = $43,026.20 So, the MIRR using the discounting approach is: 0 = -$21,971.27 + $43,026.20 / (1 + MIRR)5 $43,026.20 / $21,971.27 = (1 + MIRR)5 MIRR = ($43,026.20 / $21,971.27)1/5 - 1 MIRR = .1439, or 14.39%
Consider the following cash flows: Year Cash Flow 0 −$5,900 1 2,000 2 2,700 3 1,500 4 900 Required: What is the payback period for the above set of cash flows?
To calculate the payback period, we need to find the time that the project has recovered its initial investment. After two years, the project has created: $2,000 + 2,700 = $4,700 in cash flows. The project still needs to create another: $5,900 - 4,700 = $1,200 in cash flows. During the third year, the cash flows from the project will be $1,500. So, the payback period will be 2 years, plus what we still need to make divided by what we will make during the third year. The payback period is: Payback = 2 + ($1,200 / $1,500) Payback = 2.80 years
Kaleb Konstruction, Inc., has the following mutually exclusive projects available. The company has historically used a three year cutoff for projects. The required return is 10 percent. Year Project F Project G 0 -$ 150,000 -$ 235,000 1 78,000 54,000 2 54,000 72,000 3 68,000 103,000 4 60,000 139,000 5 54,000 156,000 Required: (a) Calculate the payback period for both projects. (b) Calculate the NPV for both projects. (c) Which project should the company accept?
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Kerron Company is presented with the following two mutually exclusive projects. The required return for both projects is 15 percent. Year Project M Project N 0 -$125,000 -$310,000 1 57,000 135,000 2 64,000 161,000 3 59,000 129,000 4 34,000 92,000 Required: (a) What is the IRR for each project? (b) What is the NPV for each project? (c) Which, if either, of the projects should the company accept?
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The Matterhorn Corporation is trying to choose between the following two mutually exclusive design projects: Year Cash Flow (I) Cash Flow (II) 0 -$65,000 -$24,000 1 24,000 8,000 2 29,000 14,500 3 36,000 12,800 Requirement 1: (a) If the required return is 11 percent, what is the profitability index for each project? (b) If the required return is 11 percent and the company applies the profitability index decision rule, which project should the firm accept? Requirement 2: (a) If the required return is 11 percent, what is the NPV for each project? (b) If the company applies the NPV decision rule, which project should it take?
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