Question

What is the expected return on a 1.97% semiannual coupon bond with a par value of $1,000 that is currently priced in the market at $894.21 but is expected to rise (or fall) to $1,091.36 within a 6-year holding period?

Answer 1

Expected Ret is the rate at which PV of Cash Inflows are equal to Bond price.

Period	CF	PVF @2.5%	Disc CF	PVF @3%	Disc CF
1	$        9.85	0.9756	$      9.61	0.9709	$      9.56
2	$        9.85	0.9518	$      9.38	0.9426	$      9.28
3	$        9.85	0.9286	$      9.15	0.9151	$      9.01
4	$        9.85	0.9060	$      8.92	0.8885	$      8.75
5	$        9.85	0.8839	$      8.71	0.8626	$      8.50
6	$        9.85	0.8623	$      8.49	0.8375	$      8.25
7	$        9.85	0.8413	$      8.29	0.8131	$      8.01
8	$        9.85	0.8207	$      8.08	0.7894	$      7.78
9	$        9.85	0.8007	$      7.89	0.7664	$      7.55
10	$        9.85	0.7812	$      7.69	0.7441	$      7.33
11	$        9.85	0.7621	$      7.51	0.7224	$      7.12
12	$        9.85	0.7436	$      7.32	0.7014	$      6.91
12	$ 1,091.36	0.7436	$ 811.49	0.7014	$ 765.46
PV of Cash Inflows			$ 912.53		$ 863.50
Bond Price			$ 894.21		$ 894.21
NPV			$   18.32		$ -30.71

Expected Ret for 6 months = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to 0.5% inc in disc rate ] * 0.5%

= 2.5% + [ 18.32 / 49.02 ] * 0.5%

= 2.5% + [ 0.37*0.5% ]

= 2.5 + 0.19%

= 2.69%

Expected Ret per anum = 2.69% * 12/6

= 5.38%

Pls comment, if any further assistance is required.