Question

3 years ago, you paid $1011 for a $1,000 par bond that has a 5% coupon with semiannual payments. You are selling it today for $998. You reinvested coupons at the 3.6% annual rate. What is your total return? (Report your answer to the nearest 0.01%, without the % symbol. E.g., if your answer is 5.1537%, enter it as 5.15.) (show work)

Answer 1

Modified IRR is the return from bond where coupons are reinvested at rate other than IRR (YTM).

Modified IRR:

It is similar to IRR. In IRR, we are assumed that intermediary cashflows are reinvested at IRR only. In MIRR, we assume that Intermediary CFs are reinvested at Reinvestment Rate rather than at IRR. Convert all cash flows in to Future value using reinvestment rate and calculate the growth rate between Current Value and Future value. That growth rate is MIRR.

Year	Bal Years	CF	FVF @3.6 %	FV of CFs
1	2	$        50.00	1.0733	$         53.66
2	1	$        50.00	1.0360	$         51.80
3	0	$   1,048.00	1.0000	$   1,048.00
Future Value of CFs				$   1,153.46

Thus $1011 has become $1153.46 over a period of 3 Years
Future Value = Cash Flow * ( 1 + r )^n
$ 1153.46 = $ 1011 ( 1 + r) ^ 3
( 1 + r) ^ 3 = $1153.46 / $ 1011
( 1 + r) ^ 3 = 1.1409
( 1 + r) = 1.1409 ^ ( 1 / 3 )
( 1 + r) = 1.0449
r = 1.0449 -1
r = 0.0449
i.e MIRR is 4.49 %

Thus Return from Bond is 4.49% per anum.