Question

5

A.

You own a portfolio that has 5,300 shares of stock A, which is priced at 12.4 dollars per share and has an expected return of 13.6 percent, and 2,000 shares of stock B, which is priced at 22.5 dollars per share and has an expected return of 8.02 percent. The risk-free return is 2.54 percent and inflation is expected to be 1.95 percent. What is the risk premium for your portfolio? Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098.

B.

You own a portfolio that has a total value of 118,000 dollars. The portfolio has 6,000 shares of stock A, which is priced at 8.9 dollars per share and has an expected return of 12.13 percent. The portfolio also has 20,000 shares of stock B, which has an expected return of 16.47 percent. The risk-free return is 4 percent and inflation is expected to be 1.06 percent. What is the risk premium for your portfolio? Answer as a rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098.

C

Oxygen Optimization stock is expected to be priced at 81.98 dollars in 1 year, pay a dividend of 4.53 dollars in 1 year, and pay a dividend of 7.5 dollars in 2 years. The stock has a risk premium of 11.17 percent, the risk-free rate is 7.81 percent, and inflation is expected to be 5.43 percent. What is the current price of Oxygen Optimization stock?

Answer 1

A.

Share	Quantity	Price	Value	Weight (w)	Expected Return (r)
A	5,300.00	12.40	65,720.00	0.59	0.1360
B	2,000.00	22.50	45,000.00	0.41	0.0802
Total			110,720.00
Inflation Rate
Portfolio return rp = (w1r1 + w2r2)		0.1133
Inflation Rate (i)				0.0195
Real rate of portfolio return (rrp)		0.0920	[(1 + rp) / (1 + i)] - 1
Risk free rate (rf)				0.0254
Real risk free rate (rrf)			0.0058	[(1 + rf) / (1 + i)] - 1
Real Risk premium (p)			0.0862	rrp - rrf
Risk premium				0.1074	[(1 + i) * (1 + p)] - 1

The risk premium for your portfolio is 0.1074.

B.

Share	Quantity	Price	Value	Weight (w)	Expected Return (r)
A	6,000.00	8.90	53,400.00	0.45	0.1213
B	20,000.00			0.55	0.1647
Total			118,000.00
Inflation Rate
Portfolio return rp = (w1r1 + w2r2)		0.1451
Inflation Rate (i)				0.0106
Real rate of portfolio return (rrp)		0.1330	[(1 + rp) / (1 + i)] - 1
Risk free rate (rf)				0.0400
Real risk free rate (rrf)			0.0291	[(1 + rf) / (1 + i)] - 1
Real Risk premium (p)			0.1040	rrp - rrf
Risk premium				0.1157	[(1 + i) * (1 + p)] - 1

The risk premium for your portfolio is 0.1157.

C.

Rate of inflation (i)	5.43%
Risk premium (p)	11.17%
Real Risk premium (rrp)	5.44%	[(1 + p) / (1 + i)] - 1
Risk free rate (rf)	7.81%
Real risk free rate (rrf)	2.26%	[(1 + rf) / (1 + i)] - 1
Real Expected Return (rR)	7.70%	rrp + rrf
Expected Return (R)	13.55%	[(1 + i) * (1 + rR)] - 1
Growth rate (g)	5.43%	Assumed to be same as inflation
Stock Price in year 1 (S1)	81.98
Earnings in year 1 (E1)	11.11	S1*R
Dividend in year 1 (D1)	4.53
Payout ratio in year 1 (b1)	0.41	D1/E1
Retention Rate in year 1 (1-b1)	0.59
Now, S1 = [E2-D2]/(R-i)
Dividend in year 2 (D2)	7.50
Earnings in year 2 (E2)	14.16	S1*(R-g) + D2
Payout ratio in year 2 (b2)	0.53
Retention Rate in year 1 (1-b2)	0.47
We assume that after year 2, dividend payout ratio will remain constant
Stock Price in year 0 (S0)	77.99	E1*(1-b1)/(1+R) + E2*(1-b2)/[(1+R)*(R-g)]

Thus, current price of Oxygen Optimization stock is $77.99 per share.