Question

if the marr is 12%, compute the value of x that makes the following two alternatives equally desirable. a b first cost $800 $1000 uniform annual benefit $230 $230 useful life, in years 5 x the answer is close to select one: 6 years 7 years 8 years 9 years

Answer 1

To make two investment alternatives equally desirable at a MARR of 12%, we calculate the present value of costs for both. Alternative A has a net benefit of -$28.904. Solving for the present value annuity factor for alternative B gives us x as close to 7 years.

Step-by-step explanation:

The question requires calculating the value of x (the useful life of alternative B) to make two investment alternatives equally desirable when considering the minimum attractive rate of return (MARR) of 12%. To do this, we compare the present value of costs for both options.

For alternative A, with a first cost of $800 and a uniform annual benefit of $230 for 5 years, the present value of costs (PVC) can be found using the present value annuity factor (PVAF). The PVAF at 12% for 5 years is approximately 3.6048. Thus, PVC for A is $800 - ($230 x 3.6048) = $800 - $828.904 = -$28.904 (a net benefit).

For alternative B, with a first cost of $1000 and a uniform annual benefit of $230 for x years, the PVC is $1000 - ($230 x PVAF). We want to set up the equation $1000 - ($230 x PVAF) = -$28.904 and solve for PVAF, which helps us determine x years by looking at PVAF tables or using a financial calculator.

After calculating, we find that the PVAF for B must be approximately 4.4737 to break even. This corresponds to the PVAF of a 7-year annuity at 12%, which means x is close to 7 years.