Question

the zambian government aprroved a k8 billion ($439 million) 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 on the 27th of july,2020.assuming that the central bank issued a 5 year 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;

1) The expected annalised fixed coupon income and yield rate on the bond

2) The present value of the investment

3) THE yeild to maturity rate of the bond

Answer 1

Part 1)
Amount to be invested = K50,000
Number of bond to be purchased = Amount to be invested/Issue price = K50,000/K77.35 = 646 bonds
Expected annualised fixed coupon income = Number of bonds*par value*Coupon rate = 646*100*11% = K7,106
Yield rate on the bond = Expected annualised fixed coupon income/amount invested = K7,106/K50,000 = 14.21%

Part 2)
Present value of the investment = Number of bond*Issue price = 646*K77.35 = K49,968.10

Part 3)

Year	Type	Cashflow	PVF @ 19%	DCF @ 19%	PVF @ 18%	DCF @ 18%
1	Coupon	11	0.8403	9.2433	0.8475	9.3225
2	Coupon	11	0.7061	7.7671	0.7182	7.9002
3	Coupon	11	0.5934	6.5274	0.6086	6.6946
4	Coupon	11	0.4987	5.4857	0.5158	5.6738
5	Coupon+Maturity	111	0.4191	46.5201	0.4371	48.5181
				75.5436		78.1092

YTM = Base rate + [(DCF @ 18%-Issue price)/(DCF @ 18%-DCF @ 19%)] = 18%+[(78.1092-77.35)/(78.1092-75.5436)] = 18%+[0.7592/2.5656] = 18%+0.3% = 18.3%