Original practice · fully worked
Original variant: break-even seed funding for a repair café
A repair café invests X now and at the beginnings of the next three years; each investment is 4% larger than the preceding one. It then earns 90 at every year-end forever, starting in year 1. At 8% effective, what X gives zero net present value?
- A
250.00 - B
275.00 - C
297.37 - D
320.00 - E
350.00
Answer and calculation
Perpetual income value 1,125 divided by the four-investment factor gives X = 297.37, choice C.
Setup
Setup
There are four investments at times zero through three and a perpetuity of income beginning at year one.
PVincome=90/0.08=1125 Model
Model
The cost present values decline geometrically by the ratio 1.04 divided by 1.08.
PVinvest=Xk=0∑3(1.04/1.08)k Compute
Compute
Their factor is 3.78321394; dividing the income value 1,125 by it yields 297.3662.
X=3.783213941125=297.3662 Answer
Answer
The break-even initial amount is 297.37, choice C.
X=297.37(C) 