Question

A government bond issued in Germany has a coupon rate of 5%, face value of euros 100 and maturing in five years. The coupon payments are made annually. Calculate the price of the bond (in euros) if the market rate of interest (yield to maturity) is 3.5%.
A. 100
B. 106.77
C. 106.33
D. none of the above

Please show work :)

Answer 1

A government bond issued in Germany has a coupon rate of 5%, face value of euros 100 and maturing in five years. The coupon payments are made annually. Calculate the price of the bond (in euros) if the market rate of interest (yield to maturity) is 3.5%.

Answer:
B. 106.77

Value of bond is the present value of future cash flows from the bond. Future cash flows from the Bond are annual coupon and redemption value at the end of maturity of bond.

Present Value of future cash inflow = Cash flow * Present Value Factor

Formula for finding present value Factor (PV Factor) is as follows

Where,

n = number of year / period

r = Discounting rate.

Calculation of Present Value of Future cash flows

year	Events	cash flows	Present value factor @ 3.5%	Present value
I	II	I11	IV	V=III*IV
1	Coupon	5	0.9662	4.831
2	Coupon	5	0.9335	4.668
3	Coupon	5	0.9019	4.510
4	Coupon	5	0.8714	4.357
5	Coupon	5	0.8420	4.210
5	Redemption value	100	0.8420	84.200
Value of the Bond (Total of present value of all future cash Flows)	106.775

Note:

Yearly Coupon = Face Value of the bond * Coupon Rate

                             = 100 * 5%

                             = 5

Calculation of Discounting Factor (Present Value Factor)

Discount Factor = 1/ (1+R) N

R = Discount Rate = Yield to Maturity = 3.5 %( i.e. = .035)

N = No of years

E.g. for year 2 Discount Factor      = 1/ (1.035)2

                                                          = 1/ (1.035) (1.035)

                                                          =   0.9335