Question

1. Time value of money: 1 point

You want to have an amount of $30,000 in five years. Calculate the amount you need to save each year in the next five years so you can achieve this goal. Assume that the interest rate is 6%, that interest is compounded annually, and that you put money into your saving account at the beginning of each year.  

2. Bond valuation: 2 points

XYZ Corporation has an outstanding 20-year bond with a $10,000 face value and a 9% coupon rate of interest (paid semiannually). The bond was issued 12 years ago.

1. If the bond’s market value is $11,000 today, then what is bond’s YTM?

2. If the bond is called in five years at a call price of $10,600, then what is the bond’s YTC?

3. Stock valuation: 2 points

XYZ Corporation just paid a dividend of $3 per share this year and plans to continue paying dividend of $3 per share for the next 3 years. After that, it plans to increase the dividend by 4% each year, for the remainder of the company’s life. If investors require a 8% rate of return to purchase XYZ’s common stock, what should be the market value of its stock today?

4. Capital asset pricing model: 3 points

Suppose the risk-free rate of return is 3.5% and the market risk premium is 7%. XYZ Company’s stock, which has a beta coefficient equal to 0.5, is currently selling for $36 per share. The company is expected to grow at a 3% rate forever, and the most recent dividend paid to stockholders was $1.75 per share.

a. Is XYZ’s stock correctly priced? That is, it the stock underpriced or overpriced or just right? Explain.

b. Calculate the company’s “correct” stock price.

5. IRR and NPV: 2 points

Year	Project A	Project B
0	-100000	-120000
1	40000	0
2	40000	-30000
3	40000	200000

1. Calculate the two projects’ IRRs.

2. Calculate the two projects’ NPV.

3. Calculate the traditional payback period for each project.

Answer 1

1) Here formula of future value of annuity due will be used
FV(annuity due) = A[1-(1/(1+r)^n / r] x (1+r)
Here A = annuity = ?
n = no of year = 5
r = rate of interest = 6%
30000 = A[1-(1/(1+6%)^5) / 6%] x (1+6%)
30000 = A[1-(1/(1+0.06)^5 / 0.06] x (1+0.06)
30000 = A[1-(1/(1.06)^5 / 0.06] x (1.06)
30000 = A[1-0.747258 / 0.06] x (1.06)
30000 = A[0.2527 / 0.06] x 1.06
30000 = A x 4.2124 x 1.06
30000 = A x 4.4651
A = 6718.77$
Thus one need to put $6718.77 into saving account at the beginning of each year.

2) Here Face value = $10000
Current market price = $11000
Interest = Face value x coupon rate
=10000 x 9% x 1/2
450$
n = number of coupon payments = 8 x 2 = 16
YTM = Interest +(Face value -current market price/n) / (Face value + current market price/2)
= 450 +(10000-11000)/16 / (10000+11000)/2
= 450 + (-1000/16) / 21000/2
=450 -62.5 / 10500
=387.5 /10500
=0.036904
Thus annual YTM = 0.036904 x 2
= 0.0738095
i.e 7.3810%

YTC = Interest +(Call price -market price/n) / (Call price -market price/2)
Here n = 5 x 2 = 10
= 450 +(10600-11000)/10 / (10600+11000)/2
= 450 + (-400/10) / 21600/2
=450 -40 / 10800
= 410 /10800
=0.0379629
Thus annual YTC = 0.0379629 x 2
= 0.075926
i.e 7.5926%

3) Lets find terminal value

Terminal value = D4/Ke-g
g = growth rate = 4%
D4 = D3(1+g)
=3(1+4%)
=3(1.04)
=3.12
Ke = required cost of capital =8%
Terminal value = 3.12/8%-4%
=3.12/4%
=78$

Statement showing price of stock now

Year	Dividend	PVIF @ 8%	PV
1	3	0.9259	2.78
2	3	0.8573	2.57
3	3	0.7938	2.38
Terminal value	78	0.7938	61.92
Price of stock today	69.65

Price of stock today = $69.65

4) First of all , lets find cost of capital
Cost of capital = Risk free rate of return + beta(Risk premium)
= 3.5% + 0.5(7%)
=3.5%+3.5%
=7%
Now lets find price of stock
Price of stock = D1/Ke-g
g = growth rate = 3%
D1 = Dividend paid(1+g)
=1.75(1+0.03)
=1.75(1.03)
=1.8025 $
Ke = cost of equity = 7%
Price of stock = 1.8025/ 7%-3%
=1.8025/4%
=45.06$

a) Thus this stock is undervalued as market price is less than price calculated above

b) Price of stock = $45.06