Financial Management Midterm Exam (Part 2)

1. 1. The Seattle Corporation has been presented with an investment opportunity that will yield cash flows of P30,000 per year in Years 1 through 4, P35,000 per year in Years 5 through 9, and P40,000 in Year 10. This investment will cost the firm P150,000 today, and the firm's cost of capital is 10 percent. Assume cash flows occur evenly during the year, 1/365th each day. What is the payback period for this investment?

A. 5.23 years

B. 4.86 years

C. 4.00 years

D. 6.12 years

E. 4.35 years

Using the even cash flow distribution assumption, the project will completely recover the initial investment after P30/P35 = 0.86 of Year 5:
Payback = 4 + = 4.86 years.

Explanation

Using the even cash flow distribution assumption, the project will completely recover the initial investment after P30/P35 = 0.86 of Year 5:
Payback = 4 + = 4.86 years.

2. 3. A project has the following cash flows: Project Year Cash Flow 0 -P3,000 1 1,000 2 1,000 3 1,000 4 1,000 Its cost of capital is 10 percent. What is the project's discounted payback period?

A. 3.00 years

B. 3.30 years

C. 3.52 years

D. 3.75 years

E. 4.75 years

Discounted
Year Cash Flow Cash Flow @ 10% Cumulative PV
0 -3,000 -3,000.00 -3,000.00
1 1,000 909.09 -2,090.91
2 1,000 826.45 -1,264.46
3 1,000 751.31 -513.15
4 1,000 683.01 169.86

After Year 3, you can see that you won’t need all of Year 4 cash flows to break even. To find the portion that you need, calculate 513.15/683.01 = 0.75. Therefore, the discounted payback is 3.75 years.

Explanation

Discounted
Year Cash Flow Cash Flow @ 10% Cumulative PV
0 -3,000 -3,000.00 -3,000.00
1 1,000 909.09 -2,090.91
2 1,000 826.45 -1,264.46
3 1,000 751.31 -513.15
4 1,000 683.01 169.86

After Year 3, you can see that you won’t need all of Year 4 cash flows to break even. To find the portion that you need, calculate 513.15/683.01 = 0.75. Therefore, the discounted payback is 3.75 years.

3. 5. As the director of capital budgeting for Denver Corporation, you are evaluating two mutually exclusive projects with the following net cash flows: Project X Project Z Year Cash Flow Cash Flow 0 -P100,000 -P100,000 1 50,000 10,000 2 40,000 30,000 3 30,000 40,000 4 10,000 60,000 If Denver's cost of capital is 15 percent, which project would you choose?

A. Neither project.

B. Project X, since it has the higher IRR.

C. Project Z, since it has the higher NPV.

D. Project X, since it has the higher NPV.

E. Project Z, since it has the higher IRR.

At a cost of capital of 15%, both projects have negative NPVs and, thus, both would be rejected.

Explanation

At a cost of capital of 15%, both projects have negative NPVs and, thus, both would be rejected.

4. Oak Furnishings is considering a project that has an up-front cost and a series of positive cash flows. The project's estimated cash flows are summarized below: Project Year Cash Flow 0 ? 1 P500 million 2 300 million 3 400 million 4 600 million The project has a regular payback of 2.25 years. What is the project's internal rate of return (IRR)?

A. 23.1%

B. 143.9%

C. 17.7%

D. 33.5%

E. 41.0%

The regular payback period is the time it takes for the project's cash flows to equal the initial investment. In this case, the regular payback period is 2.25 years. The internal rate of return (IRR) is the discount rate that makes the net present value (NPV) of the project's cash flows equal to zero. To find the IRR, we need to calculate the NPV of the cash flows at different discount rates until we find the rate that gives an NPV of zero. The IRR for this project is 33.5%, which means that at a discount rate of 33.5%, the present value of the cash flows equals the initial investment.

Explanation

The regular payback period is the time it takes for the project's cash flows to equal the initial investment. In this case, the regular payback period is 2.25 years. The internal rate of return (IRR) is the discount rate that makes the net present value (NPV) of the project's cash flows equal to zero. To find the IRR, we need to calculate the NPV of the cash flows at different discount rates until we find the rate that gives an NPV of zero. The IRR for this project is 33.5%, which means that at a discount rate of 33.5%, the present value of the cash flows equals the initial investment.

5. 2. Coughlin Motors is considering a project with the following expected cash flows: Project Year Cash Flow 0 -P700 million 1 200 million 2 370 million 3 225 million 4 700 million The project's WACC is 10 percent. What is the project's discounted payback?

A. 3.15 years

B. 4.09 years

C. 1.62 years

D. 2.58 years

E. 3.09 years

The PV of the outflows is -700 million. To find the discounted payback you need to keep adding cash flows until the cumulative PVs of the cash inflows equal the PV of the outflow:

Discounted
Year Cash Flow Cash Flow @ 10% Cumulative PV
0 -700 million -700.0000 -700.0000
1 200 million 181.8182 -518.1818
2 370 million 305.7851 -212.3967
3 225 million 169.0458 -43.3509
4 700 million 478.1094 434.7585

The payback occurs somewhere in Year 4. To find out exactly where, we calculate 43.3509/478.1094 = 0.0907 through the year. Therefore, the discounted payback is 3.091 years.

Explanation

The PV of the outflows is -700 million. To find the discounted payback you need to keep adding cash flows until the cumulative PVs of the cash inflows equal the PV of the outflow:

Discounted
Year Cash Flow Cash Flow @ 10% Cumulative PV
0 -700 million -700.0000 -700.0000
1 200 million 181.8182 -518.1818
2 370 million 305.7851 -212.3967
3 225 million 169.0458 -43.3509
4 700 million 478.1094 434.7585

The payback occurs somewhere in Year 4. To find out exactly where, we calculate 43.3509/478.1094 = 0.0907 through the year. Therefore, the discounted payback is 3.091 years.

6. 6. An insurance firm agrees to pay you P3,310 at the end of 20 years if you pay premiums of P100 per year at the end of each year for 20 years. Find the internal rate of return to the nearest whole percentage point.

A. 9%

B. 7%

C. 5%

D. 3%

E. 11%

Financial calculator solution:
Inputs: CF0 = 0; CF1 = -100; Nj = 19; CF2 = 3210. Output: IRR = 5.0%.

Explanation

Financial calculator solution:
Inputs: CF0 = 0; CF1 = -100; Nj = 19; CF2 = 3210. Output: IRR = 5.0%.

7. 10. You are considering the purchase of an investment that would pay you P5,000 per year for Years 1-5, P3,000 per year for Years 6-8, and P2,000 per year for Years 9 and 10. If you require a 14 percent rate of return, and the cash flows occur at the end of each year, then how much should you be willing to pay for this investment?

A. P15,819.27

B. P21,937.26

C. P32,415.85

D. P38,000.00

E. P52,815.71

The correct answer is b. P21,937.26. To determine the present value of the investment, we need to discount each cash flow back to its present value using the required rate of return of 14 percent. The present value of the cash flows in Years 1-5 is calculated using the formula PV = CF / (1 + r)^n, where CF is the cash flow, r is the rate of return, and n is the number of years. The present value of the cash flows in Years 6-8 and Years 9-10 are calculated in the same way. Summing up all the present values gives us the total present value of the investment, which is P21,937.26.

Explanation

The correct answer is b. P21,937.26. To determine the present value of the investment, we need to discount each cash flow back to its present value using the required rate of return of 14 percent. The present value of the cash flows in Years 1-5 is calculated using the formula PV = CF / (1 + r)^n, where CF is the cash flow, r is the rate of return, and n is the number of years. The present value of the cash flows in Years 6-8 and Years 9-10 are calculated in the same way. Summing up all the present values gives us the total present value of the investment, which is P21,937.26.

8. 8. Projects X and Y have the following expected net cash flows: Project X Project Y Year Cash Flow Cash Flow 0 -P500,000 -P500,000 1 250,000 350,000 2 250,000 350,000 3 250,000 Assume that both projects have a 10 percent cost of capital. What is the net present value (NPV) of the project that has the highest IRR?

A. P 13,626.35

B. P 16,959.00

C. P 62,050.62

D. P107,438.02

E. P121,713.00

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Explanation

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9. 9. Lloyd Enterprises has a project that has the following cash flows: Project Year Cash Flow 0 -P200,000 1 50,000 2 100,000 3 150,000 4 40,000 5 25,000 The cost of capital is 10 percent. What is the project's discounted payback?

A. 1.8763 years

B. 2.0000 years

C. 2.3333 years

D. 2.4793 years

E. 2.6380 years

The discounted payback period is the time it takes for the cumulative discounted cash flows to equal or exceed the initial investment. To calculate the discounted payback, we need to calculate the present value of each cash flow using the cost of capital of 10%. The present value of each cash flow is calculated as follows: Year 1: $50,000 / (1 + 0.10)^1 = $45,454.55 Year 2: $100,000 / (1 + 0.10)^2 = $82,644.63 Year 3: $150,000 / (1 + 0.10)^3 = $112,233.45 Year 4: $40,000 / (1 + 0.10)^4 = $28,925.62 Year 5: $25,000 / (1 + 0.10)^5 = $15,248.42 Now we can calculate the cumulative discounted cash flows: Year 1: $45,454.55 Year 2: $45,454.55 + $82,644.63 = $128,099.18 Year 3: $128,099.18 + $112,233.45 = $240,332.63 Year 4: $240,332.63 + $28,925.62 = $269,258.25 Year 5: $269,258.25 + $15,248.42 = $284,506.67 The discounted payback period is the time it takes for the cumulative discounted cash flows to equal or exceed the initial investment of $200,000. In this case, it takes approximately 2.6380 years for the cumulative discounted cash flows to equal or exceed $200,000. Therefore, the correct answer is e. 2.6380 years.

Explanation

The discounted payback period is the time it takes for the cumulative discounted cash flows to equal or exceed the initial investment. To calculate the discounted payback, we need to calculate the present value of each cash flow using the cost of capital of 10%. The present value of each cash flow is calculated as follows: Year 1: $50,000 / (1 + 0.10)^1 = $45,454.55 Year 2: $100,000 / (1 + 0.10)^2 = $82,644.63 Year 3: $150,000 / (1 + 0.10)^3 = $112,233.45 Year 4: $40,000 / (1 + 0.10)^4 = $28,925.62 Year 5: $25,000 / (1 + 0.10)^5 = $15,248.42 Now we can calculate the cumulative discounted cash flows: Year 1: $45,454.55 Year 2: $45,454.55 + $82,644.63 = $128,099.18 Year 3: $128,099.18 + $112,233.45 = $240,332.63 Year 4: $240,332.63 + $28,925.62 = $269,258.25 Year 5: $269,258.25 + $15,248.42 = $284,506.67 The discounted payback period is the time it takes for the cumulative discounted cash flows to equal or exceed the initial investment of $200,000. In this case, it takes approximately 2.6380 years for the cumulative discounted cash flows to equal or exceed $200,000. Therefore, the correct answer is e. 2.6380 years.

10. 4. Project A has a 10 percent cost of capital and the following cash flows: Project A Year Cash Flow 0 -P300 1 100 2 150 3 200 4 50 What is Project A's discounted payback?

A. 2.25 years

B. 2.36 years

C. 2.43 years

D. 2.50 years

E. 2.57 years

Discounted
Year Cash Flow Cash Flow @ 10% Cumulative PV
0 -300 -300.00 -300.00
1 100 100/(1.10) = 90.91 -209.09
2 150 150/(1.10)2 = 123.97 -85.12
3 200 200/(1.10)3 = 150.26 65.14
4 50 50/(1.10)4 = 34.15

From the cumulative cash flows we can see that the discounted payback is somewhere between 2 and 3 years. We assume that the 150.26 is received evenly throughout the third year. So, the initial outlay is recovered in 2 + 85.12/150.26, or 2.57 years.

Explanation

Discounted
Year Cash Flow Cash Flow @ 10% Cumulative PV
0 -300 -300.00 -300.00
1 100 100/(1.10) = 90.91 -209.09
2 150 150/(1.10)2 = 123.97 -85.12
3 200 200/(1.10)3 = 150.26 65.14
4 50 50/(1.10)4 = 34.15

From the cumulative cash flows we can see that the discounted payback is somewhere between 2 and 3 years. We assume that the 150.26 is received evenly throughout the third year. So, the initial outlay is recovered in 2 + 85.12/150.26, or 2.57 years.