Bangladesh University of Professionals

Assignment - 3
Title: Chapter 08 and 09
Course Title: Corporate Finance
Course Code: FIN4101

Prepared for:
Assistant Professor
MD. NAHID ALAM
Department of Finance and Banking
Faculty of Business Studies
Bangladesh University of Professionals (BUP)

Prepared by:
Section-A
MD. HABIBUR RAHMAN SAJIB
ID: 2122151111
Section: A

Date of Submission: January 2, 2025

Given Information,

Par value = € 1000

Maturity = 15 years

Coupon rate = 8.4%

YTM = 7.6% or 0.076

Coupon = (1000× 8.4% )

= 84

B = PV of Annuity + PV of Lump Sum

1
1−(1+𝑟)𝑛 𝐹𝑉
B=𝐶 ×[ ]+
𝑟 (1+𝑟)𝑛

1
1− 1000
(1+0.076)15
B= 84 × [ ]+ (1+0.076)15
0.076

= 1070.18

The current price of the bond is 1070.18.

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 Answer to question no. 2

A bond that sells at par value has the same YTM as the coupon rate. Both bonds sell at par, so the
preliminary YTM of the bond is 8% equal to the coupon rate. Both bonds consist of semi-annual
interest payments. Assuming face value = 1000

Scenario 1, when YTM suddenly rises to 10%

Laurel INC.

Maturity = 2 Years

YTM = 10%

Par value = 1000

Coupon rate = 8%

Coupon = (1000 × 8%) /2 = 40

Semi-annual, m =2

B = PV of Annuity + PV of Lump Sum

1
1− 𝑟 𝑛×𝑚
(1+ ) 𝐹𝑉
B=𝐶 ×[ 2
𝑟 ]+ 𝑟
(1+ )𝑛×𝑚
2 2

1
1−
.10 2×2
(1+ ) 1000
B = 40 × [ .10
2
]+ .10 2×2
2 (1+ )
2

B= 964.54

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Hardy Corp.

Maturity = 15 Years

YTM = 10%

Par value = 1000

Coupon rate = 8%

Coupon = (1000 × 8%) /2 = 40

Semi-annual, m =2

1
1− 𝑟 𝑛×𝑚
(1+ ) 𝐹𝑉
B =𝐶 × [ 2
𝑟 ]+ 𝑟
(1+ )𝑛×𝑚
2 2

1
1−
.10 15×2
(1+ ) 1000
B = 40 × [ 2
.10 ]+ .10 15×2
2 (1+ )
2

B = 846.28

Scenario 2, when YTM suddenly drops to 6%

Laurel INC.

Maturity = 2 Years

YTM = 6%

Par value = 1000

Coupon rate = 8%

Coupon = (1000 × 8%) /2 = 40

Semi-annual, m =2

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 1
1− 𝑟 𝑛×𝑚
(1+ ) 𝐹𝑉
B=𝐶 ×[ 2
𝑟 ]+ 𝑟
(1+ )𝑛×𝑚
2 2

1
1−
.06 2×2
(1+ )
2 1000
B = 40 × [ .06 ]+ .06 2×2
2 (1+ )
2

B = 1037.17

Hardy Corp.

Maturity = 15 Years

YTM = 10%

Par value = 1000

Coupon rate = 6%

Coupon = (1000 × 8%) /2 = 40

Semi-annual, m =2

1
1− 𝑟 𝑛×𝑚
(1+ ) 𝐹𝑉
B=𝐶 ×[ 2
𝑟 ]+ 𝑟
(1+ )𝑛×𝑚
2 2

1
1−
.06 15×2
(1+ ) 1000
B = 40 × [ 2
.06 ]+ .06 15×2
2 (1+ )
2

B = 1196.0044

For 6%

The total percentage changes in bond prices for Laurel Inc. (1037.17-1000)/1000 = 0.03717 3.72%

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The total percentage changes in bond prices for Hardy Corp. (1196.0044-1000)/1000 = 0.19600
or 19.60%

For 10%

The total percentage changes in bond prices for Laurel Inc. (954.54-1000)/1000 = -0.04546 or -
4.55%

The total percentage changes in bond prices for Hardy Corp. (846.28-1000)/1000 = -0.15372 or
-15.372%

Bond Prices vs YTM

800
600
400
200
0
6.00 8.00 10.00
YTM

Laurel Inc. Hardy Corp.

When the bond has a longer maturity period, the bond prices have great sensitivity to changes in
interest rate.

6|Page
 Answer to question no. 3

Given information,

To determine the capital gains and the current yield, we need to find the bond's price. The current
price and the price after one year is,

For Premium Bond P,

YTM = 7% or 0.07

Maturity = 5 years

Assuming face value =1000

1
1−(1+𝑟)𝑛 𝐹𝑉
𝐵0 = 𝐶 [ ]+
𝑟 (1+𝑟)𝑛

1
1− 1000
(1+0.07)5
= 90 × [ ]+ (1+0.07)5
0.07

=1082.004

1
1−(1+𝑟)𝑛 𝐹𝑉
𝐵1 = 𝐶 [ ]+
𝑟 (1+𝑟)𝑛

1
1−(1+0.07)4 1000
= 90 × [ ]+
0.07 (1+0.07)4

=1067.744

Current Yield = (90 /1082.004) × 100 = 8.32%

The Capital Gain is (1067.744 – 1082.004) /1082.004 = -0.013179 or -1.32%

7|Page
For Discount Bond D,

Assuming face value =1000

1
1− 1000
(1+0.07) 5
= 50 × [ ]+ (1+0.07)5
0.07

= 918
1
1−(1+𝑟)𝑛 𝐹𝑉
𝐵1 = 𝐶 [ ]+
𝑟 (1+𝑟)𝑛

1
1− 1000
(1+0.07) 4
= 50 × [ ]+ (1+0.07)4
0.07

= 932.26

Current Yield = (50 /918) = 0.054466 or 5.44 %

Capital gain = (932.26 -918) / 918 = 0.0155337 or 1.55%

When all parameters are held constant, a Premium bond pays a high current income but
experiences price depreciation as maturity approaches. On the other hand, a discount bond offers
lower current income but gains in price as maturity approaches. In both cases, the total return
remains at 7%, and the distribution of the returns differs, with premium bonds focusing on current
income and discount bonds focusing on capital gains.

8|Page
 Answer to question no. 04

Given Information,

Bond M,

Face value = $20000

Maturity = 20 Years

Firstly, Bond makes no payments for six years, then pays $800 for eight years semi-annually.

Secondly, Bond pays $1000 for the last remaining years semi-annually.

RRR for both bonds = 8% or 0.08

1 1
1− 1−
𝑟 𝑛 𝑟 𝑛
(1+ ) (1+ )
2 2
𝐶 𝑟 𝐶 𝑟
2 2
𝐹𝑉
B= [ 𝑟
]
+ [
𝑟
]
+ 𝑟
(1+ )𝑛 (1+ )𝑛 (1+ )𝑛
2 2 2

1 1
1− 1−
0.08 8×2 0.08 6×2
(1+ ) (1+ )
2 2
0.08 0.08
2 2 20000
B = 800 × 0.08 6×2 + 1000 × 0.08 14×2 + 0.08 20×2
(1+ ) (1+ ) (1+ )
2 2 2

[ ] [ ]
B= 5822.392+ 3129.711 +4165.78

B = 13117.88

The current price of the bond M is 13117.88

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Given information,

Bond N,

This bond has face value of $20000 and a maturity of 20 years. It provides no coupon payments.

1000
B= 0.08 20×2 = 4165.78
(1+ )
2

The current price of the bond N is 4165.78

Answer to question no. 05

Given Information,

The first amount of dividend payment = 12

Dividends will increase by $3 for each year for the next five years

RRR = 12% or 0.12

D₁ = D₀ + 3

= 12 + 3 = 15

D₂ = D₁ + 3

= 15 + 3 = 18

D₃ = D₂ + 3

= 18 + 3 = 21

D₄ = D₃ + 3

= 21 + 3 = 24

D₅ = D₄ + 3

= 24 + 3 = 27

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 15 18 21 24 27
The price of the stock, P = + + + + = 73.26
1.121 1.122 1.123 1.124 1.125

The price of the stock is 73.26.

Answer to question no. 06

a) If the company does not undertake any new investments, the stock price will be the present
value of the constant perpetual dividend. All the earnings are paid in the form of dividends.

Given information,

EPS = $9.40

RRR = 12% or 0.12

P = 9.40/ 0.12

= 78.33

b) The investment provides an increase in EPS for two years and it’s a two-year project. The
investment require EPS = $1.95 in one year. The investment will provide $2.75 and $3.05
respectively.

RRR = .12

Net present value of the returns from the project,

−1.95 2.75 3.05

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So the price of the stock will be after taking the investment opportunities,

P = 78.33+2.622

c) Since the advantages of the project ceased after two years, the EPS will be back to normal
again.

𝑃4 = 9.40 / 0.12

= 78.33

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