Answer to Question #130693 in Finance for Tila Masinge

Question

The zambian government approved a K8 billion kwacha Covid-19 bond economic stimulus package to alleviate the pandemics impact on the economy. To this effect the central bank issued K2.67 billion covid-19 bond 27th July 2020.Assuming that the central bank issued a 5yr bond with par value of K100.00 at a price of K77.35 with a 11% coupon rate, advise as an investment consultant a client who wants to invest K50,000.00
1. The expected annualized fixed coupon income and yield rate on the bond.
2. The present value of the investment
3. The yield to maturity of the bond

Answer 1

1. A bond’s coupon is the dollar value of the periodic interest payment promised to bondholders; this equals the coupon rate times the face value of the bond. For example, since the  bond issuer promises to pay an annual coupon rate of 11% to bond holders and the face value of the bond is K100, the bond holders are being promised a coupon payment of (0.11)(K100) = K11 per year.

While the yield rate of the bond will be obtained as,

$$Current\ yield=\frac{Annual\ interest\ paid}{Market\ Price} \cdot 100\%\\[5mm] Current\ yield=\frac{0.11 \cdot100}{77.35} \cdot 100\%=14.22\%\\$$

 

2. The present value of the investment

$PV=PMT \cdot [\frac{1-(1+i)^{-n}}{i}] \implies\ PV=11 \cdot [\frac{1-(1+0.11)^{-5}}{0.11}]\\ =11 \cdot [\frac{1-0.5935}{0.11}] = 11 \cdot [\frac{0.4065}{0.11}] = 11 \cdot 3.6955=40.6505$

3. The yield to maturity of the bond

$$YTM=\frac{c+\frac{FV-PV}{t}}{\frac{FV+PV}{2}}$$

Where C-Coupon Payment

FV-Face Value

PV-Present Value

t- time for security to mature

$$YTM=\frac{11+\frac{100-40.6505}{5}}{\frac{100-40.6505}{2}}=\frac{11+10.8699}{70.3253}=0.31098$$

Since the present value of the investment is a positive, then i could advise the client to invest K50,000.