An entrepreneur is looking for financing.

They are sure that their app will reach commercialization in 3.5 years. They estimate the app will be worth $500,000 by that time (Year 2.5).

Arbutus Capital offers financing to the entrepreneur. Today, they are willing to pay $100,000 for 50% of the company. That will give them a payment of 50%*$500,000 = $250,000 at Year 3.5.

What is the closest value to the EAR demanded by Arbutus as compensation for financing the entrepreneur?

Question

An entrepreneur is looking for financing.

They are sure that their app will reach commercialization in 3.5 years. They estimate the app will be worth $500,000 by that time (Year 2.5).

Arbutus Capital offers financing to the entrepreneur. Today, they are willing to pay $100,000 for 50% of the company. That will give them a payment of 50%*$500,000 = $250,000 at Year 3.5.

What is the closest value to the EAR demanded by Arbutus as compensation for financing the entrepreneur?

BlackTom AI · Accepted Answer

We start by identifying the cash flows and the investment horizon. The entrepreneur receives $100,000 today in exchange for 50% of the company. In 3.5 years, Arbutus would own 50% of a company valued at $500,000, which is $250,000 in payoff at Year 3.5.

Option 1: 25.74%. To check this, compute the effective annual rate (EAR) using the formula EAR = (Ending value / Beginning value)^(1/n) - 1. Here, Ending/Beginning = 250,000 / 100,000 = 2.5, and n = 3.5 years. So EAR = 2.5^(1/3.5) - 1. The natural log approach gives ln(2.5) ≈ 0.9163; dividing by 3.5 yields ≈ 0.2618; exponentiating gives ≈ 1.2997, and subtracting 1 yields ≈ 0.2997 or 29.97%. This is higher than 25.74%, so option 1 is not correct.

Option 2: 35.72%. Using the same calculation, EAR ≈ 29.97%, which is noticeably lower than 35.72%. Therefore option 2 overstates the required return and is incorrect.

Option 3: 29.93%. This matches the computed EAR from the cash-flow setup: EAR ≈ 2.5^(1/3.5) - 1 ≈ 0.2997, i.e., about 29.97%. Rounding to the nearest hundredth or thousandth aligns with 29.93% as the closest value among the choices.

In summary, only the third option aligns with the mathematics of converting a 2.5x total return over 3.5 years into an annualized rate, while the first two options either understate or overstate the required compensation when annualized. The core idea is to treat the investment as an initial outlay of $100,000 growing to $250,000 over 3.5 years and derive the EAR from that growth factor.

COMM_V 298 101 102 103 2025W1 Class 3 and 4 Practice Quiz

View Explanation

Log in for full answers

Similar Questions

A company is raising $65 million through commercial paper with a 60-day term at a discount rate of 1.95%. The dealer charges an annual fee of 50 basis points, and the backup credit facility costs 75 basis points per year. What is the effective annual rate of this financing?

If the bank is quoting an Annual Percentage Rate (APR) of 0.067 compounded continuously, what is the Effective Annual Rate for the year in percent (0.052 is 5.2%, so answer 5.2000) ?

If the bank is quoting an Annual Percentage Rate (APR) of 0.066 compounded continuously, what is the Effective Annual Rate for the year in percent (0.052 is 5.2%, so answer 5.2000) ?

The numbers below represent an APR and the corresponding effective annual rates when compounded semi-annually, monthly and daily. Identify the effective annual rate when compounded semi-annually. [Nothing is missing, you have enough information to figure it out.]

Calculate the effective annual rate (EAR) corresponding to the annual percentage rate (APR) of 8.14% when it is compounded 10 times a year.

If the bank is quoting an Annual Percentage Rate (APR) of 0.076 compounded continuously, what is the Effective Annual Rate for the year in percent (0.052 is 5.2%, so answer 5.2000) ?

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler