# 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?

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