Question

An investment project costs $10,000 and has annual cash flows of $2,920 for six years. a. What is the discounted payback period if the discount rate is zero percent? (Enter 0 if the project never pays back. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. What is the discounted payback period if the discount rate is 4 percent? (Enter 0 if the project never pays back. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) c. What is the discounted payback period if the discount rate is 21 percent?

Answer 1

Answer:

(A) payback in 3.42 years

(B) It doesn't payback in six years. payback is 6.66 years

Explanation:

(A) because discount rate is zero we are doing the payback period

$\frac{investment}{cashflow \: per \: year} = payback \: in \: years$

10000 investment / 2920 per year = 3.4246

(B) here there is a discount rate so we need to solve ussing the annuity formula for the time which makes the 2,920 cash flow equal to 10,000

$annuity \times \frac{1 - {1 + rate}^{ - time} }{rate} = principal$

we post our givens in the formula

we pass the annuity and rate to the second part of the equation

$1 - {1.21}^{ - time} = 10000 \: \div 290 \times .21$

10,000/2920*0.21= 0.7191...

for rounding porpuses I will refer to this as "a"

This means you have to work with the complete number, don't round it.

then, we work the equation a little more to reach this structure

${1.21}^{ - time} = 1 - a$

finally, we use log properties to solve for time

$\frac{log (1 - a)}{ log(1.21) } = - 6.662638$

-time = -6.662638

time = 6.662638

But the project life is six years... so the project doesn't payback at this discount rate.