Time Value of Money – Perpetuity

Practice Question

Intro to Finance
Time Value of Money
Perpetuity
Short Answer

The Yotsuba Group (ヨツバグループ) offers a perpetuity of $12,344 per year. However, note that the first payment will be paid in 2 years. What is the present value of the Yotsuba perpetuity if your discount rate is 12.1841% compounded annually?

Answer +
Final Answer: $90,309.04
Explanation +

Step 1: Highlight Relevant Information

- PMT (annual payment): $12,344
- First payment starts in 2 years (i.e., perpetuity starts at \( t = 2 \))
- Discount rate (EAR): 12.1841% annually

Step 2: Solve Perpetuity at t = 1

The perpetuity starts one year from now (i.e., PV1):
\[ PV_1 = \frac{PMT}{k} = \frac{12,344}{0.121841} \approx 101,312.38 \]

Step 3: Discount to Present Value at t = 0

\[ PV_0 = \frac{PV_1}{(1 + k)} = \frac{101,312.38}{1.121841} \approx 90,309.04 \]

Conclusion: Since the perpetuity starts at year 2, we calculate its value at year 1, then discount back to today. Therefore, the present value of the Yotsuba perpetuity is $90,309.04.