Question

Ms. Parvati purchased a bond at a price of Rs. 104,800 that pays a coupon of 8% and a face value of Rs 100,000. This bond matures in 5-years from now. After investing in the bond yesterday She heard about another opportunity that pays a coupon of 5% PA in the first year, 7% PA in the second year, 9% PA in the third year, 10% PA in the fourth year and finally 12% PA in the fifth year. The price of this bond is Rs. 110,000 and a maturity of 5 years. She is anxious to know whether she made a mistake buying the 8% bond.

Answer 1

Alternative available in the market is our opportuinity cost and its rate will be considered as discounting factor for calculating true value of our bond.

Example of calculating discounting rate for 5th year;

= 1/(1.012)(1.1)(1.09)(1.07)(1.05) = 0.6628

Hence answer is,

Year	Rate	Payment	Discounting factor	Present value
1	5%	₹             8,000	0.9524	₹             7,619
2	7%	₹             8,000	0.8901	₹             7,121
3	9%	₹             8,000	0.8166	₹             6,533
4	10%	₹             8,000	0.7423	₹             5,938
5	12%	₹             8,000	0.6628	₹             5,302
5	12%	₹        100,000	0.6628	₹          66,280
		Total value should have been	₹          98,794

Actual value of a bond should have been $98,794 and hence it is overpriced.

So, P has made a mistake investing in 8% bond.

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