Annie\'s Investment in Atelier\'s Bonds Call Price

Annie's Investment In Atelier's Bonds

Call price =$1,080

Call price = Face value+ interest (Extra payment to the bond holder)

Interest Income = Call Price - Face Value = $1,080 - $1,000 = $

After 5 years, Stock price = $ (30 x 50) = $1,500 If she sells the stock at the end of the 5 the year, then she will get income from sale of Stock = $ (1500-1000) = $500. Therefore, at the end of 5th year, Stock price will be greater than the Call Price and as such, the can convert the bonds into common stock.

Converting the bonds is a safe option for Annie since common stock is a safe, income-producing alternative to bonds. While convertible bonds give up some of the upside of a stock, the dividend component and the reduced volatility make them attractive investments for retirement accounts and accounts with a need for taxable income.

Question B

A. When RRR = 6%,

BO = I x PVIFA (6%, 25 yrs) + M x PVIF (6%, 25 yrs)

= 80 + 12.783 + 1000 x

= $1,255.64

B. When RRR = 8%,

BO = I x PVIFA (8%, 25 yrs) + M x PVIF (8%, 25 yrs)

= 80 + 10.675 + 1000 x 0.146

= $1,000

C. When RRR = 10%

BO = I x PVIFA (10%, 25 yrs) + M x PVIF (10%, 25 yrs)

= 80 + 9.077 + 1000 x 0.092

= $818.16

Coupon Interest Rate (CIR)

Required Rate of Return (RRR)

BO

Par Value

Analysis

Decision

8%

6%

$1,255.64

$1,000

RRR

8%

8%

$1,000

$1,000

RRR=CIR

Par Value

8%

10%

$818.16

$1,000

RRR>CIR

Discount

Question C

A. BO = [I + 2] x PVIFA (6%/2, 25 x 2 yrs) + M x PVIF (6%/2, 25 x 2 yrs.)

= [80 + 2] x 25.730 +1000 x 0.228

= $1,257.20

B. BO = [I + 2] x PVIFA (8%/2, 25 x 2 yrs) + M x PVIF (8%/2, 25 x 2 yrs.)

= 40 x 21.482 + 1000 x 0.141

= $1,000.28

C. BO = [I + 2] x PVIFA (10%/2, 25 x 2 yrs) + M x PVIF (10%/2, 25 x 2 yrs.)

= 40 x 18.256 + 1000 x 0.087

= $817.24

Annually

RRR

Semi-Annually

$1,255.64

6%

1,257.20

$1,000

8%

1,000.28

$818.16

10%

Question D

For solving this problem, it is essential that Fisher's Effect on the RRR is first taken into consideration since the correlation between RRR and inflation is not given in the case study. According to Fisher's Effect, there is a relationship between real rates, nominal rates and inflation. The Effect is given as; (1 + R) = (1 + r) (1 + h) whereby R. is the nominal rate, r is the real rate while h is the expected inflation rate.

In this regard, the coupon rate is given as 8%; so, the real rate = (8-5) % = 3%. Therefore, the inflation rate of return is calculated as shown below.

R = (1 + 0.03) x (1 +0.06) -- 1 = 9.18%

BO = I x [(1+ ?) ? - 1?

x (1+ ?) ?] + M x [1 + (1 + ?) ?]

= $80 [(1 + 0. 0918)25-1-0.0918 x (1+.0918)25] + $1,000 [1? (1 + 0.0918)25]

= 718.8979 -- 97.8891 + 111.2814

= $732.2902

For Annie's case, calculating the amount to pay for the bond is essential without which, the inflation may eat into her investment leaving her without any income. Besides, it is a common tradition for investors to calculate the amount they should pay for invested bonds.

Question E

For 8%,

BO = I x PVIFA (8%, 25 yrs) + M x PVIF (8%, 25 yrs)

= $80 x 10.675 + $1,000 x 0.146

=$1,000

For 8.75%,

BO = I x [(1+ ?) ? - 1?

x (1+ ?) ? + M x [1 + (1+ ?) ?]

= $80 [(1+0.0875)25-1-0.0875 x (1 + 0.0875)25 + 1000 [1? (1 + 0.0875)25]

= $921.2068

In this case, the RRR (8.75%) is greater than CIR (8%), so the BO ($921.2068) is less than its par value ($1,000). The effects of down rating the bond from Aa to A has several impacts on both the bond and its value. The bond will have a higher default rate, when down rated, higher premium and less liquidity. In addition, it will have higher RRR, a higher requirement for a working capital, higher cost of debts as well as higher capital costs.

Question F

When, n = (25 -- 3) yrs. = 22 yrs

BO = I x PVIFA (7%, 22 yrs) + M x PVIF (7%, 22 yrs)

= $80 x 11.061 + $1,000 x 0.226

= $1,110.88

M = $1,000

Gain = BO -- M

= $1,110.88 -- $1,000

= $110.88

Question G

When, n = (25 -- 10) yrs. = 15 yrs

BO = I x PVIFA (7%, 15 yrs) + M x PVIF (7%, 15 yrs)

= $80 x 9.108 + $1,000 x 0.362

= $1,090.64

M = $1,000

Gain = BO -- M

= $1,090.64 - $1,000

=$90.64

The maturity period in F. is lower than the maturity in G. And besides, G has a higher maturity risk as compared to F. which has a lower maturity risk. The reason for this is that the longer the maturity, the more the value of a security will change in response to a given change in interest rates.

Question H

In this situation, 983.8 = I x PVIFA kd, 25 yrs + M x PVIF kd, 25 yrs. And as such, we need to solve the equation above to determine the value of kd, which is the YTM. There are two ways this can be done by using a trial and error method as well as using a direct formula and both give answers which are almost similar.

Trial & Error

Since it is known that a required return, kd, of 8% would result in a value of $1,000, the premium rate that would result in $983.8 may be greater or less than 8%. In line with this, trying 9% will result in the following values;

= I x PVIFA (9%, 25 yrs) + M x PVIF (9%, 25 yrs)

= $80 x 9.823 + $1,000 x 0.116

= $901.84

Next we can try for 7% which brings about;

= I x PVIFA (7%, 25 yrs) + M x PVIF (7%, 25 yrs)

= $80 x 11.654 + $1,000 x 0.184

= 1116.32

Thus, LR + [(PVLR -- Market Value) / (PVLR -- PVHR)] x (HR -- LR)

= 0.07 + 132.52 / 214.48 x 0.02

= 0.0824 which comes to 8.24%

Direct Formula

YTM = (I + Discount / n) / Average Price

= [(80 + (1000 -- 983.8) / 25)] / [(1000+ 983.8) / 2

In making her decision, Annie should consider 8.24% as YTM from the bond but if the bond is of unsecured in nature, then she should consider 8.13% as YTM.

Question I