# Net Present Value and Cash Flow

**Topics:**Net present value, Cash flow, Internal rate of return

**Pages:**28 (4177 words)

**Published:**October 20, 2013

Summer 2007

August 14th. 7 -10 pm

Type A Exam

50 Multiple Choice Questions (Total of 164 marks) made up a follows 32 Calculation Questions (4 marks each for a total of 128 marks) 18 Conceptual Questions (2 marks each for a total of 36 marks) Choose the response which best answers each question. Circle your answers below, and fill in your answers on the bubble sheet. Only the bubble sheet is used to determine your exam score. BE SURE TO BLACKEN THE BUBBLES CORRESPONDING TO YOUR STUDENT NUMBER.

Please note the following points:

1) Please use your time efficiently and start with the questions that you are most comfortable with first.

2) Read the exam questions carefully;

3) Choose the answers that are closest to yours, because of possible rounding; 4) Keep at least 2 decimal places in your calculations and final answers, and at least4 decimal places for interest rates;

5) Interest rates are annual unless otherwise stated;

6) Bonds pay semi-annual coupons unless otherwise stated;

7) Bonds have a par value (or face value) of $1,000; and

8) You may use the back of the exam paper as your scrap paper. Good Luck.

32 Calculation Questions (4 marks each)

1. The common stock of Robin's Tools sells for $24.50. The firm's beta is 1.2, the riskfree rate is 4%, and the return on the market portfolio is 12%. Next year's dividend is expected to be $1.50. Assuming that dividend growth is expected to remain constant for Robin’s Tools over the foreseeable future, what is the firm's anticipated dividend growth rate?

A)

B)

C)

D)

E)

6.65%

7.48%

9.15%

13.6%

15.0%

Solution: B

r = 4% + 1.2 x (12% - 4%) = 13.6% and

$24.50 = $1.50 / (13.6% - g)

Leads to g = 7.48%

2. What is the yield to maturity on a 10-year zero-coupon bond with a $1,000 face value selling at $742?

A)

B)

C)

D)

E)

3.03%

7.42%

13.48%

34.78

42.37%

Solution: A

YTM = (1000/742) 1/10 -1 = .03029 or 3.03%

3. Consider the following monthly cash flows (see the diagram below):

X

Today

Z

X

Z

X

Z

1

2

3

4

19

20

Cash flows of an amount X are made for months 1, 3, 5, …, 17 and 19 (the ten oddnumbered months) and cash flows of an amount Z are made for months 2, 4, 6, …, 18 and 20 (the ten even-numbered months). The APR is 6% and is compounded on a monthly basis. What is the present value of these cash flows today if X = $2,000 and Z = - $700?

A) 12,311

B) 12,406

C) 25,569

D) 25,664

E) 32,955

Solution: B

The monthly interest rate is 0.5% but since the X’s cash flows are made every two months, we need to calculate the 2-months equivalent interest rate: I2m = r = (1 + 0.5%) 2 − 1 = 1.0025%

The present value of the Z’s cash flows is given by:

Using your calculator:

I2m = 1.0025%, n=10, PMT = -700, FV=0, COMP PV

PVz0 = -$6629.02 at t=0 (Since fist payment begins at t=2 and “i" is calculated for every 2 month period, and last payment is at t=20)

And the present value of the X’s is given by:

Since X begins at t=1, using your calculator for a regular annuity will give PV at t =-1: I2m = 1.0025%, n=10, PMT = 2000, FV=0, COMP PV

PVx--1 = -$18,940.07 at t= -1 (Since fist payment begins at t=1 and “i" is calculated for every 2 month period, and last payment is at t=19, you are really calculating PV of an annuity at t= -1)

To adjust for PVx at t=0-> 18,940.07 x (1.005)1 = $19,034.77 The total present value (Z + X) is equal to:

PV = $19,034.77 − $6,629.02 = $12,405.75

4. TD Bank’s earnings and dividends are expected to grow at a rate of 10% during the next 2 years, at 8% in the third year, and at a constant rate of 6% thereafter. If last dividend paid was $2.00 and the required rate of return on its common stock is 12%. How much should you pay today for one share of TD Bank?

A) $19.31

B) $24.66

C) $38.62

D) $51.93

E) $55.41

Solution: C...

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