Discount Cash Flow Applications

Question 1

Which of the following statements least accurately describes the IRR and NPV methods?

• the discount rate that gives an investment an NPV of zero is the investment’s IRR.
• For a single project, the IRR and NPV rules lead to exactly the same accept/reject decision.
• if the NPV and IRR methods give conflicting decisions for mutually exclusive projects, the IRR decision should be used to select the project.
• The NPV method assumes that a project’s cash flows will be reinvested at the cost of capital, while the IRR method assumes they will be reinvested at the IRR.

Answer 1

If the NPV and IRR methods give conflicting decisions when selecting among mutually exclusive projects, always select the project with the greatest positive NPV. (C)

Question 2

Which of the following statements least accurately describes the IRR and NPV methods?

• A project’s IRR can be positive even if the NPV is negative.
• A project with an IRR equal to the cost of capital will have an NPV of zero.
• A project’s NPV may be positive even if the IRR is less than the cost of capital.
• The NPV and IRR method can give conflicting project rankings when the project’s initials costs are of different sizes.

Answer 2

A project will have negative NPV if its IRR is less than the firm’s cost of capital. (C)

Question 3

A company is considering entering into a joint venture that will require an investment of $10 million. The project is expected to generate cash flows of $4 million, $3 million, and $4 million in each of the next three years, respectively. Assuming a discount rate of 10%, what is the project’s NPV?

Answer 3

NPV = 4/1.10 + 3/(1.10)^2 + 4/(1.10)^3 - $10 = $0.879038

CF0 = -10 
CF1 = 4 
CF2 = 3 
CF3 = 4 
I = 10 
> NPV = -0.879038 (million)

Question 4

A company is considering entering into a joint venture that will require an investment of $10 million. The project is expected to generate cash flows of $4 million, $3 million, and $4 million in each of the next three years. Assuming a discount rate of 10%, what is the project’s approximate IRR?

Answer 4

Using information from the previous question, we know that the NPV is negative at 10%. This, the IRR must be less than 10%. This leaves only choice A to be the answer. Calculator solution: IRR = 4.9%

Question 5

What should an analyst recommend based on the following information for two independent project?

Project A: 
investment at t=0 = -$3,000
cash flow at t = 1 = $5,000
IRR = 66.67% 
NPV at 12% = $1,464.29

Project B: 
investment at t=0 = -$10,000
cash flow at t = 1 = $15,000
IRR = 50.00% 
NPV at 12% = $3,392.86

• accept A and reject B
• reject A and accept B
• accept A and accept B
• reject A and reject B

Answer 5

Both projects should be accepted because both projects have positive NPVs and will thus increase shareholder wealth.

Question 6

What should an analyst recommend based on the following information for two mutually exclusive projects?

Project A: 
investment at t=0 = -$3,000
cash flow at t = 1 = $5,000
IRR = 66.67% 
NPV at 12% = $1,464.29

Project B: 
investment at t=0 = -$10,000
cash flow at t = 1 = $15,000
IRR = 50.00% 
NPV at 12% = $3,392.86

• accept A and reject B
• reject A and accept B
• accept A and accept B
• reject A and reject B

Answer 6

When the NPV and IRR rankings conflict, always select the project with the highest positive NPV in order to maximise shareholder wealth. (B)

Question 7

Goodeal, Inc., is considering the purchase of a new material handling system for a cost of $15 million. This system is expected to generate a positive cash flow of $1.8 million per year in perpetuity. What is the NPV of the proposed investment if the appropriate discount rate is 10.5%?

Answer 7

NPV = PV (cash flows) - CF0
($1.8 million / 0.105) - $15 million = $2,142,857.
Accept the project.

Question 8

Goodeal, Inc., is considering the purchase of a new material handling system for a cost of $15 million. This system is expected to generate a positive cash flow of $1.8 million per year in perpetuity. What is the IRR of the proposed investment if the appropriate discount rate is 10.5%?

Answer 8

As a perpetuity, the following relationship applies: $1.8 million / IRR = $15 million.

IRR = 1.8 / 15 = 12%
because IRR > cost of capital (hurdle rate), accept the project.

Question 9

Should a company accept a project that has an IRR of 14% and an NPV of $2.8 million if the cost of capital is 12%?

• Yes, based only on the NPV
• Yes, based only on the IRR
• Yes, based on the NPV and the IRR
• No, based on both the NPV and IRR

Answer 9

The project should be accepted on the basis of its positive NPV and its IRR, which exceeds the cost of capital. (C)

Question 10

Which of the following statements least likely represents a characteristic of the time-weighted rate of return? it is:

• not affected by the timing of cash flow
• industry’s preferred method for performance measurement.
• used to measure the compound rate of growth of $1 over a stated measurement period
• defined as the internal rate of return on an investment portfolio, taking into account all inflows and outflows.

Answer 10

The money-weighted rate of return is the IRR of an investment’s net cash flows. (D)

Question 11

Assume an investor purchases a share of stock for $50 at time t = 0, and another share at $65 at the time t = 1 and at the end of year 1 and year 2, the stock paid a $2 dividend. Also, at the end of year 2, the investor sold both shares for $70 each.

The money-weighted rate of return on the investment is:

Answer 11

One way to do this problem is to set up the cash flows so that the PV of inflows = PV of outflows and plug in each of the multiple choices 50 + 65 / (1 - t) = 2 / (t + r) + 144 / (1 + r)^2 > t = 18.02%.

CF > 2nd > CLR WORK 
50 (+/-) ENTER 
\/ 63 (+/-) ENTER 
\/ \/ 144 ENTER 
IRR  CPT

Question 12

Assume an investor purchases a share of stock for $50 at time t = 0, and another share at $65 at the time t = 1 and at the end of year 1 and year 2, the stock paid a $2 dividend. Also, at the end of year 2, the investor sold both shares for $70 each.

The time-weighted rate of return on the investment is:

Answer 12

HPR(1) = (65 + 2) / 50 - 1 = 34%

HPR (2) = (140 + 4) / 130 - 1 = 10.77%

Time weighted return = ((1.34)(1.1077))^0.5 - 1 = 21.83%

Question 13

What is the bank discount yield for a T-bill that is selling for $99,000, with a face value of $100,000 and 95 days remaining until maturity?

Answer 13

(1000 / 100,000) x (360 / 95) = 3.79%

Question 14

What is the holding period yield for a T-bill that is selling for $99,000 with a face value of $100,000 and 95 days remaining until maturity?

Answer 14

(100,000 - 99,000) / 99,000 = 1.01%

Question 15

What is the effective annual yield for a T-bill that is selling for $99,000 with a face value of $100,000 and 95 days remaining until maturity?

Answer 15

(1 + 0.0101)^365/95 - 1 = 3.94%

Question 16

What is the money market yield for a T-bill that is selling for $99,000 with a face value of $100,000 and 95 days remaining until maturity?

Answer 16

(360 x 0.0379) / 360 - (95 x 0.0379) = 3.83%

or
1,000 / 99,000) (360 / 95

Question 17

Which of the following is least accurate regarding the bank discount yield?

• It assumes a 360-day year.
• it ignores the opportunity to earn compound interest.
• it is based on the face value of the bond, not its purchase price.
• it reflects the nonannulaised return an investor will earn over a security’s life.

Answer 17

This is actually the definition of the holding period yield. The other answers are true statements regarding the bank discount yield. (D)

Question 18

A 175 day T-bill has an effective annual yield of 3.80%. Its money-market yield is closest to:

Answer 18

because the effective yield is 3.8%, we know (1000/price)^365/175 = 1.038

(1000/1.038)^365/175 = 982.28

The money market yield is

(360 / 175) x HPY = (360/175) (1000/982.28 - 1) = 360/175 (0.01804) = 3.711%

Alternatively, we can get the HPY from the EAY of 3.8% as (1.038)^175/365 - 1= 1.804%