You can pay $10,000 cash today for a home repair, or finance it at 0% interest with payments of $500/month for 20 months (also totaling $10,000). From an NPV perspective, which is the better option if your discount rate is 6%/year?
AThey are equivalent — both total $10,000 in payments, so neither is better
BFinancing is better — future payments are worth less than $10,000 in today's dollars, so their NPV is below $10,000
CPaying cash is always better because you avoid debt and the uncertainty it creates
DFinancing is worse because you remain in debt longer, which always destroys value
At a 6% discount rate, $500 paid 1 month from now is worth slightly less than $500 today; $500 paid 20 months from now is worth considerably less. Discounting all 20 payments to present value gives a total less than $10,000 — meaning the financing option costs less in today's dollars than paying cash upfront. This is the fundamental insight: nominal totals are the wrong comparison; NPV converts everything to present-value terms. Option A is the common error of ignoring time value.
Question 2 Multiple Choice
Two investments: Option A pays $5,000 in 1 year; Option B pays $5,500 in 5 years. With a 10% annual discount rate, which has higher net present value?
AOption B — it pays more total dollars
BOption A — the money arrives sooner and is discounted less, so its present value is higher
CThey are approximately equal — the extra $500 in Option B compensates for the delay
DCannot be determined without knowing the investor's risk tolerance
Option A: PV = $5,000 / 1.10 ≈ $4,545. Option B: PV = $5,500 / 1.10⁵ ≈ $5,500 / 1.611 ≈ $3,414. Despite paying $500 more in nominal terms, Option B's present value is nearly $1,100 lower than Option A's because of the additional 4 years of discounting. This illustrates how powerfully time affects present value at a 10% rate — a 5-year wait nearly halves the present value of the cash flow.
Question 3 True / False
A higher discount rate makes future cash flows worth less in present value terms, which is why high-interest debt is particularly destructive — the interest rate effectively works as a discount rate compounding against you.
TTrue
FFalse
Answer: True
Correct. When you owe money at a high interest rate, the future payments you must make are being 'inflated' by that rate, not discounted. From your perspective as the borrower, the interest rate is the cost that makes your future obligations larger and larger. From the lender's perspective, a high discount rate makes your promised future payments less valuable — which is why high-risk borrowers pay higher rates. The two perspectives are mirrors of each other.
Question 4 True / False
NPV analysis typically determines definitively which financial decision is better because it fully accounts for most relevant factors including risk and certainty.
TTrue
FFalse
Answer: False
NPV calculates expected economic value under a chosen discount rate, but it does not account for risk preferences or certainty differences. A guaranteed 6% return (paying off a mortgage) may rationally be worth more to a risk-averse person than an uncertain 8% stock market return, even though the stock investment has higher expected NPV. NPV tells you which option has higher expected economic value — it does not tell you which option is better for your specific risk tolerance, emotional peace of mind, or liquidity needs.
Question 5 Short Answer
Why is the discount rate the most important and most subjective input in an NPV calculation?
Think about your answer, then reveal below.
Model answer: The discount rate represents your opportunity cost — what you could earn by deploying that money elsewhere. It determines how much each future dollar is 'shrunk' back to present value. A small change in the discount rate can flip which option has the higher NPV, especially for cash flows far in the future. It is subjective because different people genuinely have different opportunity costs depending on what investment alternatives are available to them, their risk tolerance, and their financial situation.
This subjectivity is not a flaw in NPV — it is the framework surfacing the correct question: compared to what? A person who can reliably earn 10% in their business should use a 10% discount rate, making future money worth much less to them. A person with no investment alternatives should use a low rate, making future money nearly as valuable as present money. NPV forces you to be explicit about your opportunity cost, which is the comparison that matters for financial decisions.