Original practice · fully worked
Original variant: perpetual cooperative patronage payments
A farm cooperative pays 100 immediately and 100 six months later. Starting one year from now, payments are 150, 200, 250, and so on forever at six-month intervals. At 3% per half-year, calculate the present value.
- A
50,000.00 - B
55,555.56 - C
58,988.89 - D
60,500.00 - E
65,000.00
Answer and calculation
Separating the delayed level and increasing components gives 58,988.89, choice C.
Setup
Setup
The first two payments are valued separately because the arithmetic pattern begins only at the third payment.
Model
Model
From year one onward, split the stream into a level 150 perpetuity and a 50-per-period increasing component.
PV=100+100v+v2(1−v150+(1−v)250v) Compute
Compute
Discounting that combined perpetuity by two half-years and adding the first two payments gives 58,988.8889.
PV=58988.8889 Answer
Answer
The present value is 58,988.89, so choice C is correct.
PV=58988.89(C) 