This Exam FM sample reference tests Reinvestment-Adjusted Net Present Value. The present value of proceeds is 100,699, so net present value is 699. The result agrees with the published answer key, choice C.
How to solve this Reinvestment-Adjusted Net Present Value question
Setup
Setup
Move the time-3 receipt forward one year at its stated reinvestment rate, then combine it with the time-4 receipt. This places all terminal proceeds at one date.
60000 at t=3⟹62400 at t=4
Model
Model
The combined time-4 amount is 122,400. Discount that amount four years at 5% and subtract the initial 100,000 outlay.
PV=122400(1.05)−4=100699
Compute
Compute
The present value of proceeds is 100,699, so net present value is 699.
NPV=100699−100000=699
Answer
Answer
The calculation gives 699 for reinvestment-adjusted net present value, matching published choice C.
NPV=699(C)
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These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A (–1,398) does not match the checked reinvestment-adjusted net present value result (699); no distinct standard one-step error is identifiable.
BChoice B (–699) does not match the checked reinvestment-adjusted net present value result (699); no distinct standard one-step error is identifiable.
DChoice D (1,398) does not match the checked reinvestment-adjusted net present value result (699); no distinct standard one-step error is identifiable.
EChoice E (2,629) does not match the checked reinvestment-adjusted net present value result (699); no distinct standard one-step error is identifiable.
Original practice · fully worked
Original variant: reinvested launch receipts
A project costs 50,000 now and pays 30,000 at the ends of years 2 and 3. The year-2 receipt reinvests at 3%, and valuation uses 4%. Find the NPV.
A 3000
B 3800
C 4140
D 4500
E 5000
Variant answer in brief
Net present value is 4,139.878, or 4,140. This selects choice C.
Setup
Setup
Carry the time-2 receipt to time 3 at 3%, then combine it with the time-3 receipt.
FV3=30000(1.03)+30000=60900
Model
Model
Discount the 60,900 terminal proceeds three years at 4% and subtract the initial 50,000.
PV=60900(1.04)−3=54139.878
Compute
Compute
Net present value is 4,139.878, or 4,140.
NPV=4139.878
Answer
Answer
The requested value is 4140, so the correct choice is C.
The 2210-page Financial Mathematics Proof Manual reorganizes 461 verified Exam FM solutions by syllabus skill and adds formula proofs, error patterns, and original worked practice.
