Question

Q1. Consider the concepts of yield to maturity (YTM) and realised yield (RY) for a bond. Note that both YTM and RY indicate returns for an investor upon his/her investment (i.e. purchase) depending on whether he/she waits until maturity or sells the bond early.

Suppose an investor bought a 10-year maturity zero-coupon bond 5 years ago for $710.

Currently the bond is priced $850 in the market.

The investor is deciding between two choices:

i. Selling the bond now at the stated current market price.

ii. Waiting until the bond matures.

Assume interest on the bond is compounded annually. The face value of the bond is $1,000.

Which choice will provide a better return for the investor?

Q3(c)
A German company is expecting to grow at a rate of 10% in the first two years and by 5% in the following year. Followed by this, the company expects to settle to a constant growth rate of 2%. The company has paid €2 as a dividend per share recently.
The investor’s required rate of return for the share is 17% p.a., and the market price for the stock is currently €14 per share.
Determine the value of this share. Is the share a desirable purchase?

Answer 1

Solution 1) Option 1) Sell the bond immediately at the current rate of $850

Realized Yield (RY) can be calculated as:

850 = 710*(1 + RY)^5

(1 + RY)^5 = 850/710 = 1.197183

RY = (1.197183)^(1/5) - 1

RY = 1.03665 - 1

RY = 0.03665 = 3.665%

Option 2) Waiting until the bond matures with the Face Value of $1,000

Realized Yield (RY) can be calculated as:

1000 = 710*(1 + RY)^10

(1 + RY)^10 = 1000/710

RY = (1000/710)^(1/10) - 1

RY = 1.034842 - 1

RY = 0.034842 = 3.4842%

Since, Realized Yield for Option 1 is greater, thus, investor should sell the bond immediately for Option 1.

Solution 3)c) Recent Dividend (D0) = €2

Growth in dividend in next two years = 10%

Dividend in year 1 (D1) = Dividend in year 0*(1 + growth rate)

Dividend in year 1 (D1) = 2*(1 + 10%) = 2*1.1 = 2.2

Dividend in year 2 (D2) = Dividend in year 1*(1 + growth rate)

Dividend in year 2 (D2) = 2.2*(1 + 10%) = 2.42

Growth rate in the third year = 5%

Dividend in year 3 (D3) = Dividend in year 2*(1 + growth rate)

Dividend in year 3 (D3) = 2.42*(1+5%) = 2.541

Growth rate in the fourth year and forward = 2%

Dividend in year 4 (D4) = Dividend in year 3*(1 + growth rate)

Dividend in year 4 (D4) = 2.541*(1+2%) = 2.59182

D4 will continue to grow till perpetuity

According the Gordon Growth Model, the present value of perpetual cash flows = Expected Dividend next year/(Required return - Perpetual Growth Rate)

Required rate of return for the share is 17%

Stock Price is calculated as follows:

Current Market Price of the stock = €14

Since the market price of the stock is less than the intrinsic value of the stock, hence, investor should purchase the stock.