Question

You will be evaluating three projects for Hasbro Toys. Hasbro's cost of capital or discount rate is 10%. The first project (A) will cost $25,000 initially. The project will then return cash flows of $8,000 for 4 years. The second project (B) will cost $40,000 initially. The project will then return cash flows of $15,000 for the next 2 years and $10,000 for 2 years after that. The third project (C) will cost $30,000 initially. The project will then return cash flows of $12,000 for 3 years

What is Projects B's NPV, IRR, Payback Period, and PI? Show step by step and circle final answer.

Answer 1

Project B:
Given that the cost of capital or discount rate=10%
Cash flows for project B is given by:
Initial investment in year 0: $40,000
Year 1:$15,000
Year 2:$15,000
Year 3:$10,000
Year 4:$10,000

Net present value or NPV calculation:
NPV=-initial investment + Present value of future cash flows

Present value of future cash flows=Cash flow in year 1/(1+Discount Rate)^1+Cash flow in year 2/(1+Discount Rate)^2+Cash flow in year 3/(1+Discount Rate)^3+Cash flow in year 4/(1+Discount Rate)^4
NPV=-$40,000+$15,000/(1+10%)^1+$15,000/(1+10%)^2+$10,000/(1+10%)^3+$10,000/(1+10%)^4
=-$40,000+$15,000/(1.1)^1+$15,000/(1.1)^2+$10,000/(1.1)^3+$10,000/(1.1)^4
=-$40000+$15000/1.1+$15000/1.21+$10000/1.331+$10000/1.4641

=-$40000+$13636.36364+$12396.69421+$7513.148009+$6830.134554

NPV=$376.340413

Internal rate of return or IRR calculation:

Cash flows for project B is given by:
Year 0: $40,000
Year 1:$15,000
Year 2:$15,000
Year 3:$10,000
Year 4:$10,000

We can use these values and calculate IRR using excel.

IRR=10.47%

Payback period calculation:

Net cash flows:
Year 0:-$40,000
Year 1:$15,000
Year 2:$15,000
Year 3:$10,000
Year 4:$10,000
As the initial investment is a cash outflow, we have shown it with a negative sign

Cumulative net cash flows:
Year 0:-$40,000
Year 1:$15,000-$40,000=-$25000
Year 2:$15,000-$25000=-$10000
Year 3:$10,000-$10000=0
Year 4:$10,000
Payback period=Full years until recovery+(Unrecovered cost at the beginning of last year)/(Cash flow during the last year)
Full years until recovery=3
Unrecovered cost at the beginning of last year=0, so second part of the equation will become zero.
Payback period=3 years

Profitability Index calculation:

Profitability index=Present value of future cash flows/Initial investment
Cash flows after the initial investment are given by:
Year 1:$15,000
Year 2:$15,000
Year 3:$10,000
Year 4:$10,000

Present value of future cash flows=Cash flow in year 1/(1+Discount Rate)^1+Cash flow in year 2/(1+Discount Rate)^2+Cash flow in year 3/(1+Discount Rate)^3+Cash flow in year 4/(1+Discount Rate)^4
$15,000/(1+10%)^1+$15,000/(1+10%)^2+$10,000/(1+10%)^3+$10,000/(1+10%)^4
=$15,000/(1.1)^1+$15,000/(1.1)^2+$10,000/(1.1)^3+$10,000/(1.1)^4
=$15000/1.1+$15000/1.21+$10000/1.331+$10000/1.4641
=$13636.36364+$12396.69421+$7513.148009+$6830.134554
=$40376.34041
Initial investment in year 0 is $40,000
Profitability index=$40376.34041/$40,000=1.00940851