Question

You are negotiating to make a 7-year loan of $25,000 to Breck Inc. To repay you, Breck will pay $2,000 at the end of Year 1, $5,000 at the end of Year 2, and $7,000 at the end of Year 3, plus a fixed but currently unspecified cash flow, X, at the end of each year from Year 4 through Year 7. Breck is essentially riskless, so you are confident the payments will be made. You regard 7.5% as an appropriate rate of return on a low risk but illiquid 7-year loan. What cash flow must the investment provide at the end of each of the final 4 years, that is, what is X?

Answer 1

		7.50%
Year	Cash Flow	PV factor = 1/ (1+r)^t	PV
0	$                    (25,000.00)	1.000	$(25,000.00)
1	$                        2,000.00	0.930	$    1,860.47
2	$                        5,000.00	0.865	$    4,326.66
3	$                        7,000.00	0.805	$    5,634.72
4	$                                    -	0.749	$                -
5	$                                    -	0.697	$                -
6	$                                    -	0.648	$                -
7	$                                    -	0.603	$                -
		Total	$(13,178.15)
	So the PV of annual payments from T4 to T7 should be equal to 13,178.15
	Assumed annual payment	X
	Sum of PV factor from T4-T7	2.696
	X*2.6960755814896=	$   13,178.15
	Annual payment=	13178.15/2.6960755814896
	Annual payment=	$     4,887.90