Part 3 of 3

A Canadian bank offers the company a loan in EUR to the company, at the EUR effective annual rate of 3%, such that the company will repay exactly $8,000,000 EUR in one year (principal + interest). What is the NPV of the order to the company if they take the loan?

Round your answer to two decimals. That is, $193,030.1123 should be entered as 193030.11

Question

Part 3 of 3

A Canadian bank offers the company a loan in EUR to the company, at the EUR effective annual rate of 3%, such that the company will repay exactly $8,000,000  EUR in one year (principal + interest). What is the NPV of the order to the company if they take the loan?

Round your answer to two decimals. That is, $193,030.1123 should be entered as 193030.11

BlackTom AI · Accepted Answer

We need to restate the problem clearly and then work through how to compute the NPV step by step, noting any missing information that would affect the numeric result.

Restating the question and data:
- A Canadian bank offers a loan to the company in EUR.
- The loan terms are an EUR effective annual rate of 3%.
- The company will repay exactly 8,000,000 EUR in one year (principal + interest).
- The task is to compute the NPV of taking this loan for the company, with the final answer rounded to two decimals as specified in the problem.

Key formula and concept to apply:
- For a single-period loan with a principal L today and repayment R at t = 1, the loan’s NPV to the borrower (the company) is typically the present value of the cash inflow (the loan proceeds) minus the present value of the repayment, both discounted or converted consistently to a common currency.
- If we ignore currency exchange issues (i.e., work entirely in EUR), then the loan proceeds today should equal some amount L such that the repayment in one year equals L grown at the loan rate: R = L × (1 + r). In the given terms, R = 8,000,000 EUR and r = 0.03, so L = 8,000,000 / 1.03.
- The NPV in EUR would then be NPV_EUR = L − 8,000,000 / 1.03 = L − L = 0. So, under a fair-rate, single-period loan with repayment exactly at the loan rate, the EUR NPV would be zero if we measure everything in EUR and use the same discount/loan rate.

However, a crucial missing element:
- The problem states the company is Canadian. To compute a numeric NPV in a single currency (e.g., CAD), we would need the EUR/CAD exchange rate today (and whether to use spot or forward) to convert the EUR cash flows to CAD (or vice versa).
- Additionally, if the company’s own cost of capital (or discount rate in CAD terms) differs from 3% EUR, we would discount the EUR cash flows at the appropriate CAD rate to obtain CAD NPV.
- Without the exchange rate (and the domestic discount rate in CAD), we cannot produce the exact CAD NPV numeric value. The given numeric answer (2,339,805.83) implies a specific exchange-rate and/or domestic discounting convention that isn’t provided in the prompt.

Proceeding with step-by-step calculations under the EUR-only interpretation (to illustrate the method):
1) Compute the amount borrowed today in EUR that would lead to a repayment of 8,000,000 EUR in one year at 3%:
   L = 8,000,000 / 1.03 ≈ 7,766,990.29 EUR
2) Compute the EUR NPV of taking the loan, if measured in EUR and using the same discount rate 3%:
   NPV_EUR = L − 8,000,000 / 1.03 = 7,766,990.29 − 7,766,990.29 = 0 EUR
   (This reflects a fair loan at the stated rate; there is no arbitrage profit in pure EUR terms.)

If the problem instead intends the NPV in CAD terms, or uses a different convention (e.g., you receive EUR now and discount the EUR cash flows at a CAD rate by converting currencies), you would:
- Convert the EUR loan proceeds L_EUR to CAD using the current EUR/CAD spot (or forward) rate: L_CAD = L_EUR × S_EURCAD.
- Compute the CAD cash outflow in one year: 8,000,000 EUR × S_EURCAD = R_CAD.
- Discount R_CAD back to today using the CAD discount rate (or the company’s WACC in CAD): NPV_CAD = L_CAD − R_CAD discounted to today. If you apply a single-period discount at the CAD rate i_CAD, you’d have NPV_CAD = L_CAD − R_CAD / (1 + i_CAD).

Conclusion about the numeric answer provided (2,339,805.83):
- The value 2,339,805.83 cannot be validated without the EUR/CAD exchange rate and the CAD discount rate used in the calculation. The EUR-only logic yields zero NPV, while a CAD-denominated NPV would depend entirely on the currency conversion inputs and the CAD discount rate chosen by the problem designer.

Summary of what would be needed to confirm the numeric result:
- The EUR/CAD spot (or forward) exchange rate to convert between EUR and CAD.
- The CAD-based discount rate (or the company’s cost of capital in CAD terms) to discount the EUR cash flows into CAD terms.
- With those two pieces, follow the steps: convert L_EUR to L_CAD, convert 8,000,000 EUR to R_CAD, and compute NPV_CAD = NPV of receiving L_CAD today and paying R_CAD in one year at the CAD discount rate.

If you can provide the exchange rate and the CAD discount rate used for the calculation, I can recompute the exact NPV value in CAD and verify whether it matches 2,339,805.83.

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