Question

Which is the value of this bond?
maturity is 5 years from now; nominal is 6.000 euros and the coupon is 5%?
The market interest rate is 4% for this combination of issuer and maturity.
Annual coupo 6,000 5.0%
t Ct 1+i (1+i)^t Ct/(1+i)^t
1 300 104.0% 1.04 288
2 300 104.0% 1.08 277
3 300 104.0% 1.12 267
4 300 104.0% 1.17 256
5 6,300 104.0% 1.22 5,178
6,267
What would be different if the market asked for a higher interes
rate (5%) or for a lower interest rate (3%)?

Answer 1

Annual coupon payments = 5% of Euro 6,000 = Euro 300

Now value of bond = present value of all future coupon payments and maturity amount that will be discounted at 4%. Maturity amount = Euro 6,000 and so cash flow in 5th year = 6,000+300 = 6,300

Year	Cash flow	1+r	PVIF	PV = cash flow*PVIF
1	300	1.04	0.9615	288.46
2	300		0.9246	277.37
3	300		0.8890	266.70
4	300		0.8548	256.44
5	6,300		0.8219	5,178.14
			Total	6,267.11

Thus price = Euro 6,267.11

When interest rate is 5%

Year	Cash flow	1+r	PVIF	PV = cash flow*PVIF
1	300	1.05	0.9524	285.71
2	300		0.9070	272.11
3	300		0.8638	259.15
4	300		0.8227	246.81
5	6,300		0.7835	4,936.21
			Total	6,000.00

When rate is 3%

Year	Cash flow	1+r	PVIF	PV = cash flow*PVIF
1	300	1.03	0.9709	291.26
2	300		0.9426	282.78
3	300		0.9151	274.54
4	300		0.8885	266.55
5	6,300		0.8626	5,434.44
			Total	6,549.56

Thus prices at different rates are:

Rate	Price
4%	6,267.11
5%	6,000.00
3%	6,549.56