Question

Q4

5.What is the price of a zero-coupon 24-year maturity bond per face (par) value of $1,000 if the annual market rates for these bonds are 5.9%? Answer to the nearest cent, xxx.xx and enter without the dollar sign.

6.A firm's stock has 50% chance of a 8% rate of return and a  50% chance of a 23% rate of return. What is the standard deviation of return for this stock? Answer as a percent return  to the nearest hundredth of a percent as in xx.xx without entering a percent symbol.  

Answer 1

5) Price of zero coupon bond:

M = Face/Par value = 1,000

r = rate of interest = 5.9%

n= number of years until maturity = 24 years

Price of zero coupon bond = M/(1+r)^n

= 1,000/(1+0.059)^24

= 1,000/(1.059)^24

= 1,000/3.958

= 252.65

Price of zero coupon bond = 252.65 (without dollar sign)

6) Calculation of Expected return

Stock	Probability (1)	Return (2)	Expected return (3) (1*2)
A	0.5	8%	4%
B	0.5	23%	11.5%
		Expected return	15.5%

Calculation of standard deviation of stock:

Probability (1)	Return-Expected return (2)	Square of Return-Expected return (3)	Variance (4) (1*3)
0.5	8%-15.5%=-7.5% or -0.075	(-0.075)^2 = 0.0056	0.0028
0.5	23%-15.5%= 7.5% or 0.075	(0.075)^2 = 0.0056	0.0028
		Variance	0.0056

Standard deviation = Square root of Variance

= Square root of 0.0056

= 0.0748 or 7.48 (without percentage symbol)

Standard deviation of stock = 7.48