# Internal Rate of Return Comparisons

Course: Fundamentals of Financial Planning

Lesson 5b: Using the HP 10b-II Calculator

## Student Question:

For number 2 (below), should there be a CF of zero for Company B year one? It appears the explanation skips this cash flow.

**Bobby is investigating the cost of an alarm system for his home, which he thinks he will own for three years. Company A will charge him an installation fee of $500 when the system is installed at the beginning of the first year; they will charge an annual service fee of $480 at the beginning of each of the three years for monitoring service. Company B will charge him $1,300 when the system is installed at the beginning of the first year; they will charge no service fee for the first year, the second year service will cost $380, and the third year service will cost $480. Bobby’s cost of capital is 9%. Which company’s plan is more cost effective?**

**Provided Answer:**

Follow these keystrokes to get the answer:

First calculate the NPV for the Company A Plan:

[keystrokes: Shift C ALL | 980 +/- CFj | 480 +/- CFj 2 Shift Nj | 9 I/YR | Shift NPV ]**The NPV of the Company A Plan = -1, 824.37**

Next, calculate the NPV for the Company B Plan:

[keystrokes: Shift C ALL | 1,300 +/- CFj | 380 +/- CFj | 480 +/- CFj | 9 I/YR | Shift NPV ]**The NPV of Company B = -2,052.63**

Therefore, Company A’s proposal is the least costly.

## Instructor Response:

Hi Lizzie-

These cash flows can be confusing. The feedback for the answer is accurate because there was no service fee in Year 1 when it was installed. Now had there been a service fee in Year 1, we would have added that to the $1,300 cash flow (installation) that starts it off. Look at our calculation for Company A. It has a $480 service fee for 3 years, but you only see 2 cash flows of $480. And that’s because we’ve combined the Year 1 service fee with the initial $500 fee, for a total first cash flow of $980.

Hope that helps!

*Dan*