Question

I need solutions for these practices questions

True/False

1. If the interest rate (or discount rate) is positive, the future value of an expected series of payment will always exceed the present value of the same series.

2. If semiannual compounding is used, the effective annual interest rate (EAI) is equal to the nominal annual rate.

3. You are able to buy a stock at $14 where as its intrinsic value (or fair value) is $14.01. You have indeed bought this stock at a bargain price.

4. Company ABC is expected to pay a dividend of $1.00 per year forever. You should be willing to pay up to $5 to buy a share of this company if your required return is 20%.

5. A company is expected to pay a dividend of $2/share at the end of year 1 and no dividends thereafter. You will be willing to pay up to $1.81 for one share if your required return is 10%.

6. You will write a call option if you are confident that the stock will not go up and believe that it will not fall drastically. Perhaps there will be little variation in stock price.

7. You are writing a put option on underlying British Pounds. It means that you are taking a long position.

8. Under constant growth, the DCF model growth rate can exceed the required return.

9. Writing put option on an underlying index limits your profit to the premium received, but the risk increases as stock rises.

Please choose the BEST answer.

10. What is the Present Value given the following information?

                                                                             

                                                                              End of year

                                 Year                APR                  CFs

                                    1                   5%                   $100

                                    2                   5%                   $200

                                    3                   5%                   $200

                                    4                   7%                   $100

                                    5                   7%                   $300

                                    6                   8%                   $400

                                    7                   8%                   $400

1. 1124
2. 1294
3. 1424
4. 1524

11. Assume that you will receive $2,000 a year in Years 1 through 5, $3,000 a year in Years 6 through 8, and $4,000 in Year 9, with all cash flows to be received at the end of the year. If you require a 14 percent rate of return, what is the present value of these cash flows?

1. $ 9,851
2. $13,250
3. $11,714
4. $15,129
5. $17,353

12. If a 5-year ordinary annuity has a present value of $1,000, and if the interest rate is 10 percent, what is the amount of each annuity payment?

1. $240.42
2. $263.80
3. $300.20
4. $315.38
5. $346.87

13. In 1958 the average tuition for one year at an Ivy League school was $1,800. Thirty years later, in 1988, the average cost was $13,700. What was the average annual compounded growth rate in tuition over the 30-year period?

13. 1. 12%
    2. 9%
    3. 6%
    4. 7%
    5. 8%
14. You have the opportunity to buy perpetuity that pays $1,000 annually. Your required rate of return on this investment is 15 percent. You should be essentially indifferent to buying or not buying the investment if it were offered at a price of

1. $5,000.00
2. $6,000.00
3. $6,666.67
4. $7,500.00
5. $8,728.50

15. South Penn Trucking is financing a new truck with a loan of $10,000 to be repaid in 5 annual end-of-year installments of $2,504.56. What annual interest rate is the company paying?    

1.   7%
2.   8%
3.   9%
4. 10%
5. 11%

16. You just put $1,000 in a bank account that pays 6 percent nominal annual interest, compounded monthly. How much will you have in your account after 3 years?

1. $1,006.00
2. $1,056.45
3. $1,180.32
4. $1,191.00
5. $1,196.68

17. Assume that you plan to buy a share of XYZ stock today and to hold it for 2 years. Your expectations are that you will not receive a dividend at the end of Year 1, but you will receive a dividend of $9.25 at the end of Year 2. In addition, you expect to sell the stock for $150 at the end of Year 2. If your expected rate of return is 16 percent, how much should you be willing to pay for this stock today?

1. $164.19
2. $ 75.29
3. $107.53
4. $118.35
5. $131.74

18. Conner Corporation has a stock price of $32.35 per share. The last dividend was $3.42 (i.e., D₀ = $3.42). The long-run growth rate for the company is a constant 7 percent. What is the company’s capital gains yield and expected dividend yield?

1. Capital gains yield = 7.00%; expected dividend yield = 10.57%.
2. Capital gains yield = 10.57%; expected dividend yield = 7.00%.
3. Capital gains yield = 7.00%; expected dividend yield = 4.31%.
4. Capital gains yield = 11.31%; expected dividend yield = 7.00%.
5. Capital gains yield = 7.00%; expected dividend yield = 11.31%.

19. The last dividend paid by Klein Company was $1.00. Klein’s growth rate is expected to be a constant 5 percent for 2 years, after which dividends are expected to grow at a rate of 10 percent forever. Klein’s required rate of return on equity (k_s) is 12 percent. What is the current price of Klein’s common stock?

1. $21.00
2. $33.33
3. $42.25
4. $50.16
5. $58.75

20. What is the fair value of stock (FIN 361) given the following information: D₀ = $4, required rate of return = 10%, growth rate in dividends = year 1 (-20%), year 2 (56%), year 3 (26%) and year 4 (0%).

1. 8.33
2. 12.33
3. 16.33
4. 20.33
5. 24.33

21. You write a December 2015 call on XYZ at an exercise price of $50. You receive a premium of $10. The market price does not exceed $45 until the new year (January 2016). Your profit or loss will be

1. $50
2. $45
3. $10
4. $5
5. $0

Answer 1

1.If the interest rate (or discount rate) is positive, the future value of an expected series of payment will always exceed the present value of the same series.

TRUE---as Present value is discounting to the present,

Whereas

FV is compounding the amounts at the given interest rates.

2.If semiannual compounding is used, the effective annual interest rate (EAI) is equal to the nominal annual rate.

FALSE--- Effective Annual Rate(EAR)=(1+semi-annual Rate)^2-1

EAI will always be slightly more ,for ex. (1+(10%/2))^2-1=10.25%

3.You are able to buy a stock at $14 where as its intrinsic value (or fair value) is $14.01. You have indeed bought this stock at a bargain price.

TRUE-- mathematically

4.Company ABC is expected to pay a dividend of $1.00 per year forever. You should be willing to pay up to $5 to buy a share of this company if your required return is 20%.

TRUE---- Present value or Price of the stock=1/20%=$ 5

5.A company is expected to pay a dividend of $2/share at the end of year 1 and no dividends thereafter. You will be willing to pay up to $1.81 for one share if your required return is 10%.

TRUE--PV of the dividend cash flow at end Yr.1 at 10% reqd. return= 2/1.1^1=1.81

6.You will write a call option if you are confident that the stock will not go up and believe that it will not fall drastically. Perhaps there will be little variation in stock price.

TRUE

7.You are writing a put option on underlying British Pounds. It means that you are taking a long position.

FALSe--Writing both a call or put option is a short position as the writer is obligated to sell or buy (respectively) the shares fom the long position holder, or buyer of the same.

8. Under constant growth, the DCF model growth rate can exceed the required return.

FALSE-   Under the constant growth model,Cost of equity=(D0*(1+g))/(r-g)

If the growth rate exceeds the reqd. return, cost of equity will be negative, which cannot happen.

9.Writing put option on an underlying index limits your profit to the premium received, but the risk increases as stock rises.

TRUE-- as worst-come-worst , the put writer may have to buy the stock ,in which case the loss is higher

10.Year	APR	CFs	PV F for r%,yr.=n		PV (CF*PV F)
1	5%	100	1/1.05^1=	0.95238	95
2	5%	200	1/1.05^2=	0.90703	181
3	5%	200	1/1.05^3=	0.86384	173
4	7%	100	1/1.07^4=	0.76290	76
5	7%	300	1/1.07^5=	0.71299	214
6	8%	400	1/1.08^6=	0.63017	252
7	8%	400	1/1.08^7=	0.58349	233
	Total PV				1225
	Nearest answer = b. 1294

11.Year	CFs	PV F at 14%	PV
1	2000	0.877193	1754
2	2000	0.7694675	1539
3	2000	0.6749715	1350
4	2000	0.5920803	1184
5	2000	0.5193687	1039
6	3000	0.4555865	1367
7	3000	0.3996373	1199
8	3000	0.3505591	1052
9	4000	0.3075079	1230
PV of the cash flows=			11714
ANSWER: c.. 11714

12. 1000=Pmt.*(1-1.1^-5)/0.1

pmt.= 263.80

ANSWER: b. $263.80

13.1800*(1+g)^30=13700

((13700/1800)^(1/30))-1=

g=7%

ANSWER: d. 7%

14. Price of a perpetuity = 1000/15%= 6666.67

ANSWER: c. 6667.67

15. PV of ordinary annuity

10000=2504.56*(1-(1+r)^-5)/r

r=8%

ANSWER: b. 8%

16. Amt. at end of 3 yrs.=1000*(1.005)^36=

1196.68

ANSWER: e. $ 1196.68

17.Equating the cash flows to 0

-x+(9.25/1.16^2)+(150/1.16^2)=0

x= 118.35

ANSWER: d. 118.35

18. Growth rate g= Capital gains Yield ,ie. 7%

Div. Yield= 3.42/32.35=10.57%

So, ANSWER: a.

a. Capital gains yield = 7.00%; expected dividend yield = 10.57%.

19..
Div.Yr.	Dividend Cash flow		PV at 12%
D1	1*(1.05)=	1.05	0.9375
D2	1.05*1.05=	1.1025	0.878906
D2	(1.1025*1.105)/(12%-10%)=	60.6375	48.33984
Sum of future C/Fs=Current price			50.16
ANSWER: d. $ 50.16
20..
Div.Yr.	Dividend Cash flow		PV at 10%
D1	4*(1-0.20)=	3.2	2.909091
D2	3.2*1.56=	4.992	4.12562
D3	4.992*1.26=	6.28992	4.72571
D4	6.28992	6.28992	4.2961
Sum of future C/Fs=Current price			16.05652
ANSWER: c. 16.33
21.ANSWER: c. $ 10
Mkt.price 45< strike price 50
so, premium received is the writer's profit.