CF CH 9

It will cost $6,000 to acquire an ice cream cart. Cart sales are expected to be $3,600 a year for three years. After the three years, the cart is expected to be worthless as the expected life of the refrigeration unit is only three years. What is the payback period?

1.67 years Payback period = $6,000 / $3,600 = 1.67 years

An investment project has annual cash inflows of $5,100, $6,200, $7,000, and $8,300, and a discount rate of 18 percent. Required: What is the discounted payback period for these cash flows if the initial cost is $8,000? (Do not round your intermediate calculations.)

1.83 years When we use discounted payback, we need to find the value of all cash flows today. The value today of the project cash flows for the first four years is: Value today of Year 1 cash flow = $5,100/1.18 = $4,322.03 Value today of Year 2 cash flow = $6,200/1.182 = $4,452.74 Value today of Year 3 cash flow = $7,000/1.183 = $4,260.42 Value today of Year 4 cash flow = $8,300/1.184 = $4,281.05 To find the discounted payback, we use these values to find the payback period. The discounted first year cash flow is 4,322.03, so the discounted payback for an $8,000 initial cost is: Discounted payback = 1 + ($8,000 − 4,322.03)/$4,452.74 = 1.83 years

In actual practice, managers most frequently use which two types of investment criteria?

IRR and NPV.

The internal rate of return:

Is easy to understand.

What is the net present value of a project with the following cash flows and a required return of 14 percent? Year Cash Flow 0 -$36,600 1 17,100 2 24,530 3 4,150

$76.17

An investment project costs $17,800 and has annual cash flows of $4,400 for six years. Required : (a) What is the discounted payback period if the discount rate is zero percent? 4.05 (b) What is the discounted payback period if the discount rate is 6 percent? 4.78 (c) What is the discounted payback period if the discount rate is 19 percent? Never

(a): R = 0%: ($17,800 / $4,400) = 4.05 years discounted payback = regular payback = 4.05 years (b): R = 6%: 4400/1.06 + 4400/1.062 + 4400/1.063 + 4400/1.064 = $15,246.46 $4,400/1.065 = $3,287.94 discounted payback = 4 + ($17,800 - 15,246.46) / $3,287.94 = 4.78 years (c): R = 19%: $4,400(PVIFA19%, 6) = $15,003.02 The project never pays back.

An investment project has an installed cost of $518,297. The cash flows over the four-year life of the investment are projected to be $287,636, $203,496, $103,802, and $92,556, respectively. What is the NPV of this project if the discount rate is infinite?

-$518,297 If the discount rate is infinite, the NPV will equal the cash flow at Time 0

The relevant discount rate is 14 percent for a project with cash flows of -$9,800, $4,600, $3,300, and $3,800 for Years 0 to 3, respectively. What is the profitability index?

.93 PVInflows =$4,600 / 1.14 + $3,300 / 1.142 + $3,800 / 1.143 = $9,139.22 PI = $9,139.22 / $9,800 = .93

What is the profitability index for an investment with the following cash flows given a 9 percent required return? Year Cash Flow 0 -$24,000 1 9,200 2 11,500 3 10,900

1.11 PI = [$9,200 / (1 + 0.09) + $11,500 / (1 + 0.09)2 + $10,900 / (1 + 0.09)3] / $24,000 = 1.11

What is the internal rate of return on an investment with the following cash flows? Year Cash Flow 0 -$103,000 1 42,400 2 38,500 3 48,600

12.08 percent NPV = $0 = -$103,000 + $42,400 / (1 + r) + $38,500 / (1 + r)2 + $48,600 / (1 + r)3 IRR is the discount rate that makes NPV equal zero. To solve for r, you need to use trial-and-error, a financial calculator, or a computer. r = 12.08 percent (rounded)

A project produces annual net income of $18,200, $21,800, and $22,900 over its three-year life, respectively. The initial cost is $197,000, which is depreciated straight-line to a zero book value over three years. What is the average accounting rate of return if the required discount rate is 14.5 percent?

21.29 percent AAR = [$18,200 + 21,800 + 22,900) / 3] / [($197,000 + 0) / 2] = .2129, or 21.29%

You're trying to determine whether or not you should expand your business at a fixed asset cost of $4.3 million. The firm uses straight-line depreciation to zero over the project life. The projected annual net income is $595,000, $502,000, $486,000, and $324,000 over these four years. What is the average accounting return?

22.17 percent AAR = [($595,000 + 502,000 + 486,000 + 324,000) / 4] / [($4,300,000 + 0) / 2] AAR = 22.17 percent

What is the payback period for the following set of cash flows? Year Cash Flow 0 −$ 7,100 1 1,300 2 2,100 3 1,800 4 2,400

3.79 years To calculate the payback period, we need to find the time that the project has recovered its initial investment. After three years, the project has created: $1300 + $2100 + $1800 = $5200 in cash flows. The project still needs to create another: $7,100 − 5,200 = $1,900 in cash flows. During the fourth year, the cash flows from the project will be $2,400. So, the payback period will be 3 years, plus what we still need to make divided by what we will make during the fourth year. The payback period is: Payback = 3 + ($1,900 / $2,400) = 3.79 years

A project with financing type cash flows is typified by a project that has which one of the following characteristics?

A cash inflow at time zero.

Project A has an initial cost of $80,000 and provides cash inflows of $34,000 a year for three years. Project B has an initial cost of $80,000 and produces a cash inflow of $114,000 in year 3. The projects are mutually exclusive. Which project(s) should you accept if the discount rate is 11.7 percent? What if the discount rate is 13.5 percent?

Accept A at 11.7 percent and neither at 13.5 percent.

Isaac has analyzed two mutually exclusive projects that have 3-year lives. Project A has an NPV of $81,406, a payback period of 2.48 years, and an AAR of 9.31 percent. Project B has an NPV of $82,909, a payback period of 2.57 years, and an AAR of 9.22 percent. The required return for Project A is 11.5 percent while it is 12 percent for Project B. Both projects have a required AAR of 9.25 percent. Isaac must make a recommendation and justify it in 15 words or less. What should his recommendation be?

Accept Project B and reject Project A based on the NPVs.

Rossiter Restaurants is analyzing a project that requires $180,000 of fixed assets. When the project ends, those assets are expected to have an aftertax salvage value of $45,000. How is the $45,000 salvage value handled when computing the net present value of the project?

Cash inflow in the final year of the project.

The internal rate of return is defined as the:

Discount rate which causes the net present value of a project to equal zero.

Which one of the following is an advantage of the average accounting return method of analysis?

Easy availability of information needed for the computation.

Slow Ride Corp. is evaluating a project with the following cash flows: Year Cash Flow 0 -$13,000 1 6,000 2 6,600 3 6,100 4 5,000 5 -4,700 The company uses a 11 percent discount rate and an 8 percent reinvestment rate on all of its projects. Calculate the MIRR of the project using all three methods using these interest rates. Required: (a) MIRR using the discounting approach.(Do not round your intermediate calculations.) 19.09% (b) MIRR using the reinvestment approach.(Do not round your intermediate calculations.) 13.32% (c) MIRR using the combination approach.(Do not round your intermediate calculations.) 12.92%

Explanation (a): In the discounting approach, we find the value of all cash outflows at time 0 at the discount rate, while any cash inflows remain at the time at which they occur. So, discounting the cash outflows to time 0, we find: Time 0 cash flow = $-13,000 - $4,700 / 1.115 Time 0 cash flow = $-15,789.22 So, the MIRR using the discounting approach is: 0 = $-15,789.22 + $6,000/(1+MIRR) + $6,600/(1+MIRR)2 + $6,100/(1+MIRR)3 + 5,000/(1+MIRR)4 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: MIRR = 19.09% (b): In the reinvestment approach, we find the future value of all cash except the initial cash flow at the end of the project using the reinvestment rate. So, reinvesting the cash flows to time 5, we find: Time 5 cash flow = $6,000(1.084) + $6,600(1.083) + $6,100(1.082) + $5,000(1.08) - $4,700 Time 5 cash flow = $24,292.07 So, the MIRR using the discounting approach is: 0 = $-13,000 + $24,292.07/(1+MIRR)5 $24,292.07/ $13,000 = (1+MIRR)5 MIRR = ($24,292.07 / $13,000)1/5 - 1 MIRR = 0.1332 or 13.32% (c): In the combination approach, we find the value of all cash outflows at time 0 using the discount rate, and the value of all cash inflows at the end of the project using the reinvestment rate. So, the value of the cash flows is: Time 0 cash flow = $-13,000 - $4,700 / 1.115 Time 0 cash flow = $-15,789.22 Time 5 cash flow = $6,000(1.084) + $6,600(1.083) + $6,100(1.082) + $5,000(1.08) Time 5 cash flow = $28,992.07 So, the MIRR using the discounting approach is: 0 = $-15,789.22 + $28,992.07/(1+MIRR)5 $28,992.07 / $15,789.22 = (1+MIRR)5 MIRR = ($28,992.07/ $15,789.22)1/5 - 1 MIRR = 0.1292 or 12.92%

Slow Ride Corp. is evaluating a project with the following cash flows: Year Cash Flow 0 -$29,200 1 11,400 2 14,100 3 16,000 4 13,100 5 -9,600 The company uses a 9 percent interest rate on all of its projects. Calculate the MIRR of the project using all three methods. Required: (a) MIRR using the discounting approach.(Do not round your intermediate calculations.) 19.18% (b) MIRR using the reinvestment approach. (Do not round your intermediate calculations.) 14.73% (c) MIRR using the combination approach. (Do not round your intermediate calculations.) 13.8%

Explanation (a): 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 = $29,200 - $9,600 / 1.095 Time 0 cash flow = $35,439.34 So, the MIRR using the discounting approach is: 0 = $35,439 + $11,400/(1+MIRR) + $14,100/(1+MIRR)2 + $16,000/(1+MIRR)3 + 13,100/(1+MIRR)4 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: MIRR = 19.18% (b): 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 = $11,400(1.094) + $14,100(1.093) + $16,000(1.092) + $13,100(1.09) - $9,600 Time 5 cash flow = $58,040.54 So, the MIRR using the discounting approach is: 0 = $29,200 + $58,040.54/(1+MIRR)5 $58,040.54 / $29,200 = (1+MIRR)5 MIRR = ($58,040.54 / $29,200)1/5 - 1 MIRR = 0.1473 or 14.73% (c): 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 = $29,200 - $9,600 / 1.095 Time 0 cash flow = $35,439.34 Time 5 cash flow = $11,400(1.094) + $14,100(1.093) + $16,000(1.092) + $13,100(1.09) Time 5 cash flow = $67,640.54 So, the MIRR using the discounting approach is: 0 = $35,439.34 + $67,640.54/(1+MIRR)5 $67,640.54 / $35,439.34 = (1+MIRR)5 MIRR = ($67,640.54 / $35,439.34)1/5 - 1 MIRR = 0.138 or 13.8%

A project has an initial cost of $27,400 and a market value of $32,600. What is the difference between these two values called?

Net present value.

Which one of the following methods determines the amount of the change a proposed project will have on the value of a firm?

Net present value.

A project has projected cash flows of -$148,500, $32,800, $64,200, -$7,500 and $87,300 for years 0 to 4, respectively. Should this project be accepted based on the combination approach to the modified internal rate of return if both the discount rate and the reinvestment rate are 12.6 percent? Why or why not?

No; The MIRR is 8.81 percent.

Samuelson Electronics has a required payback period of three years for all of its projects. Currently, the firm is analyzing two independent projects. Project A has an expected payback period of 2.8 years and a net present value of $6,800. Project B has an expected payback period of 3.1 years with a net present value of $28,400. Which projects should be accepted based on the payback decision rule?

Project A only.

The Square Box is considering two independent projects, both of which have an initial cost of $18,000. The cash inflows of Project A are $3,000, $7,000, and $10,000 over the next three years, respectively. The cash inflows for Project B are $3,000, $7,000, and $15,000 over the next three years, respectively. The required return is 12 percent and the required discounted payback period is 3 years. Based on discounted payback, which project(s), if either, should be accepted?

Project A should be rejected and Project B should be accepted.

You are considering two mutually exclusive projects. Both projects have an initial cost of $52,000. Project A produces cash inflows of $25,300, $37,100, and $22,000 for years 1 through 3, respectively. Project B produces cash inflows of $43,600, $19,800 and $10,400 for years 1 through 3, respectively. The required rate of return is 14.2 percent for Project A and 13.9 percent for Project B. Which project should you accept and why?

Project A; because it has the larger NPV.

You are considering two mutually exclusive projects. Project A has cash flows of -$87,000, $32,600, $35,900, and $43,400 for years 0 to 3, respectively. Project B has cash flows of -$85,000, $14,700, $21,200, and $89,800 for years 0 to 3, respectively. Project A has a required return of 9 percent while Project B's required return is 11 percent. Which project(s), if either, should you accept based on net present value?

Reject Project A and accept Project B

The Green Fiddle is considering a project that will produce sales of $87,000 a year for the next four years. The profit margin is 6 percent, the project cost is $96,000, and depreciation is straight-line to a zero book value over the life of the project. The required accounting return is 11 percent. This project should be _____ because the AAR is _____ percent.

Rejected; 10.88

Applying the discounted payback decision rule to all projects may cause:

Some positive net present value projects to be rejected.

If a project has a net present value equal to zero, then:

The project earns a return exactly equal to the discount rate.

A project has a net present value of zero. Which one of the following best describes this project?

The project's cash inflows equal its cash outflows in current dollar terms.

You are considering two mutually exclusive projects. Project A has cash flows of -$74,900, $18,400, $26,300, and $57,100 for years 0 to 3, respectively. Project B has cash flows of -$79,000, $18,400, $22,700, and $51,500 for years 0 to 3, respectively. Both projects have a required return of 12.75 percent. Should you accept or reject these projects based on the profitability index?

You should not use PI; use a different method of analysis.

A project that provides annual cash flows of $2,700 for 7 years costs $10,400 today. Required: (a) If the required return is 10 percent, what is the NPV for this project? $2,744.73 (b) Determine the IRR for this project. 17.63%

(a): The NPV of a project is the PV of the outflows minus by the PV of the inflows. Since the cash inflows are an annuity, the equation for the NPV of this project at an 10 percent required return is: NPV = -$10,400 + $2,700(PVIFA0.10%, 7) = $2,744.73 At an 10 percent required return, the NPV is positive, so we would accept the project. (b): We would be indifferent to the project if the required return was equal to the IRR of the project, since at that required return the NPV is zero. The IRR of the project is: 0 = -$10,400 + $2,700(PVIFAIRR, 7) IRR = 17.63%

For the following set of cash flows, Year Cash Flow 0 -$7,300 1 3,500 2 6,800 3 6,400 Required: (a) What is the NPV at a discount rate of 0 percent? (b) What is the NPV at a discount rate of 12 percent? (c) What is the NPV at a discount rate of 19 percent? (d) What is the NPV at a discount rate of 24 percent?

(a): The NPV of a project is the PV of the outflows minus the PV of the inflows. At a zero discount rate (and only at a zero discount rate), the cash flows can be added together across time. So, the NPV of the project at a zero percent required return is: NPV = -$7,300 + 3,500 + 6,800 + 6,400 = $9,400.00 (b): The NPV at a 12 percent required return is: NPV= -$7,300 + $3,500/1.12 + $6,800/1.122 + $6,400/1.123 = $5,801.31 (c): The NPV at a 19 percent required return is: NPV = -$7,300 + $3,500/1.19 + $6,800/1.192 + $6,400/1.193 = $4,240.96 (d): And the NPV at a 24 percent required return is: NPV = -$7,300 + $3,500/1.24 + $6,800/1.242 + $6,400/1.243 = $ 3,301.78 Notice that as the required return increases, the NPV of the project decreases. This will always be true for projects with conventional cash flows. Conventional cash flows are negative at the beginning of the project and positive throughout the rest of the project.

Consider the following two mutually exclusive projects: Year Cash Flow (A) Cash Flow (B) 0 -$244,387 -$15,100 1 29,900 4,327 2 50,000 8,724 3 53,000 13,285 4 410,000 8,444 Whichever project you choose, if any, you require a 6 percent return on your investment. Required: (a) What is the payback period for Project A? (b) What is the payback period for Project B? (c) What is the discounted payback period for Project A? (d) What is the discounted payback period for Project B? (e) What is the NPV for Project A? (f) What is the NPV for Project B ? (g) What is the IRR for Project A? (h) What is the IRR for Project B? (i) What is the profitability index for Project A? (j) What is the profitability index for Project B?

(a): The payback period for project A: 3 + ($111,487/$410,000) = 3.27 years (b): The payback period of project B: 2 + ($2,049/$13,285) = 2.15 years (c): The discounted payback for project A: $29,900/1.06 + $50,000/1.062 + $53,000/1.063 = $117,207.19 $410,000/1.154 = $324,758.4 Discounted payback = 3 + ($244,387 - 117,207.19)/$324,758.4 = 3.39 years (d): The discounted payback for project B: $4,327/1.06 + $7,764/1.062 = $11,846.4 $8,444/1.153 = $11,154.34 Discounted payback = 2 + ($15,100 - 11,846.4)/$11,154.34 = 2.29 years (e): The NPV for project A: NPV = -$244,387 + $29,900/1.06 + $50,000/1.062 + $53,000/1.063 + $410,000/1.064 NPV = $197,578.59 (f): The NPV for project B: NPV = -$15,100 + $4,327/1.06 + $8,724/1.062 + $13,285/1.063 + $8,444/1.064 NPV = $14,589.19 (g): The IRR for project A: $244,387 = $29,900/(1+IRR) + $50,000/(1+IRR)2 + $53,000/(1+IRR)3 + $410,000/(1+IRR)4 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 26% (h): The IRR for project B: $15,100 = $4,327/(1+IRR) + $8,724/(1+IRR)2 + $13,285/(1+IRR)3 + $8,444/(1+IRR)4 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 38% (i): The profitability index for project A: PI = ($29,900/1.06 + $50,000/1.062 + $53,000/1.063 + $410,000/1.064) / $244,387 = 1.808 (j): The profitability index for project B: PI = ($4,327/1.06 + $8,724/1.062 + $13,285/1.063 + $8,444/1.064) / $15,100 = 1.966

Year Cash Flow 0 −$8,100 1 3,300 2 2,500 3 3,200 Required : (a) What is the profitability index for the cashflows if the relevant discount rate is 8 percent? $0.955 (b) What is the profitability index for the cashflows if the relevant discount rate is 16 percent? $0.834 (c) What is the profitability index for the cashflows if the relevant discount rate is 24 percent? 0.736

(a): The profitability index is defined as the PV of the cash inflows divided by the PV of the cash outflows. The equation for the profitability index at a required return of 8 percent is: PI = [$3,300/1.08 + $2,500/1.082 + $3,200/1.083] / $8,100 = 0.955 (b): The equation for the profitability index at a required return of 16 percent is: PI = [$3,300/1.16 + $2,500/1.162 + $3,200/1.163] / $8,100 = 0.834 (c): The equation for the profitability index at a required return of 24 percent is: PI = [$3,300/1.24 + $2,500/1.242 + $3,200/1.243] / $8,100 = 0.736

Mahjong, Inc., has identified the following two mutually exclusive projects: Year Cash Flow (A) Cash Flow (B) 0 -$37,300 -$37,300 1 19,660 7,180 2 15,170 13,680 3 12,660 20,160 4 9,660 24,160 Required: (a) What is the IRR for Project A? 22.56% (b) What is the IRR for Project B? 21.74% (c) If the required return is 11 percent, what is the NPV for Project A? $8,344.25 (d) If the required return is 11 percent, what is the NPV for Project B? $10,927.22 (e) At what discount rate would the company be indifferent between these two projects? 19.58%

Explanation (a): The IRR is the interest rate that makes the NPV of the project equal to zero. The equation for the IRR of Project A is: 0 = -$37,300 + $19,660/(1+IRR) + $15,170/(1+IRR)2 + $12,660/(1+IRR)3 + $9,660/(1+IRR)4 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 22.56% (b): The equation for the IRR of Project B is: 0 = -$37,300 + $7,180/(1+IRR) + $13,680/(1+IRR)2 + $20,160/(1+IRR)3 + $24,160/(1+IRR)4 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 21.74% (c): The NPV of Project A is: NPVA = -$37,300 + $19,660/1.11+ $15,170/1.112 + $12,660/1.113 + $9,660/1.114 NPVA = $8,344.25 (d): And the NPV of Project B is: NPVB = -$37,300 + $7,180/1.11 + $13,680/1.112 + $20,160/1.113 + $24,160/1.114 NPVB = $10,927.22 (e): To find the crossover rate, we subtract the cash flows from one project from the cash flows of the other project. Here, we will subtract the cash flows for Project B from the cash flows of Project A. Once we find these differential cash flows, we find the IRR. The equation for the crossover rate is: Crossover rate: 0 = $12,480/(1+R) + $1,490/(1+R)2 - $7,500/(1+R)3 - $14,500/(1+R)4 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: R = 19.58% At discount rates above 19.58% choose project A; for discount rates below 19.58% choose project B; indifferent between A and B at a discount rate of 19.58%.