Question

A)Broke Benjamin Co. has a bond outstanding that makes semiannual payments with a coupon rate of 5.8 percent. The bond sells for $974.17 and matures in 14 years. The par value is $1,000. What is the YTM of the bond?

3.04%

5.77%

6.08%

5.47%

4.56%

b)The common stock of Eddie's Engines, Inc., sells for $27.51 a share. The stock is expected to pay a dividend of $2.40 per share next year. Eddie's has established a pattern of increasing their dividends by 4.5 percent annually and expects to continue doing so. What is the market rate of return on this stock?

5.55%

18.76%

11.46%

13.22%

8.72%

c)Kindzi Co. has preferred stock outstanding that is expected to pay an annual dividend of $4.60 every year in perpetuity. If the required return is 4.49 percent, what is the current stock price?

$95.62

$98.05

$107.05

$92.20

$102.45

Answer 1

Solution:-

a) Ans:- 6.08%

b) Ans:- 13.22%

C)Ans:- $102.45

Calculations are shown below :-

a) Calculation of YTM bond

Current price of bond = $974.17

Par value= $1000

Coupon rate= 5.8%

Semiannual interest= $1000*5.8%*1/2 = $29

Number of periods (n) = 14*2 = 28 periods

Calculation of YTM if it is selling at $974.17

            We will use hit and trail method to calculate the YTM .

First we take discount rate 3% as discount rate ,

            Price of bond = 29*PVIFA(3%,28)+1000*PVIF(3%,28)

                                    = 29*18.76410823+1000*0.437076753

                                    =$981.24

Now we will assume discount rate to be 4%.

Price of bond = 29*PVIFA(4%,28)+1000*PVIF(4%,28)

                                    = 29*16.66306322+1000*0.333477471

                                    = $816.71

Now YTM of bond can be calculated as follows

Hal yearly YTM=Lower DR+Difference b/w DRs{[PV of lower DR-PV]/Absolute difference B/w DRs}

Where, DR stands for discount rate

            PV stands for present value

            B/W stands for between.

Now substituting the value

Half yearly YTM = 3%+1%*981.24-974.17)/(981.24-816.71)

            =3%+0.04%

            =3.04%

Hence the YTM = 2*3.04%= 6.08%

b) Calculation of market return on equity .

Using DDM we have

Price of share = DPS₁/(K_e-g)

Where

Price of share = $27.51

DPS₁= $2.40

g= 4.5%

putting the values ,

27.51=2.40/(K_e-0.045)

K_e-0.045= 2.40/27.51

K_e=13.22%

Hence the market rate of return on stock is = 13.22%

c) Current price of preferred stock = Preferred dividend/ required return

                                                                =$4.60/0.0449

                                                                =$102.45

Please feel free to ask if you have any query in the comment section.