Your firm has the opportunity to invest $90,000 in a new project opportunity but due to cash flow concerns, your boss wants to know when you can pay back the original investment. Using the discounted payback method, you determine that the project should generate inflows of $30,000, $35,000, $30,000, $25,000, and $20,000 respectively for an expected five years after completion of the project. Your firm's required rate of return (ror) is 10%. Calculate how long it should take to pay back the initial project investment. [Hint: List your all cash flow by year, investment can be seen as happening in year zero, calculate the NPV of inflow using Discount factor = 1/(1 + ror)^t, find the nearest break-even year using accumulated cash flow, then find the decimal point assuming cash flow are evenly distributed within a year]

3.67 years

Explanation:

Cashflow by year

Year 0 $90,000(Investment)

Year 1 $30,000

Year 2 $35,000

Year 3 $30,000

Year 4 $25,000

Year 5 $20,000

Rate of return(ror) = 10%= 0.1

Calculating Net present value(NPV) using discount factor ;

Discount factor = 1/(1 + ror)^t

YEAR 1

Discount factor:

1/(1 + 0.1) = 1/1.1 =0.9

NPV = 0.9 × $30,000 = $27,000

YEAR 2

Discount factor:

1/(1 + 0.1)^2 = 1/1.1^2 =0.83

NPV = 0.826 × $35,000 = $29,050

YEAR 3

Discount factor:

1/(1 + 0.1)^3 = 1/1.1^3 =0.75

NPV = 0.75 × $30,000 = $22,500

YEAR 4

Discount factor:

1/(1 + 0.1)^4 = 1/1.1^4 =0.68

NPV = 0.68 × $25,000 = $17,000

YEAR 5

Discount factor:

1/(1 + 0.1)^5 = 1/1.1^5 =0.62

NPV = 0.62 × $20,000 = $12,400

Year 1: $90,000 - $27,000 = $63,000

Year 2: $63,000 - $29,050 = $33,950

Year 3: $33,950 - $22,500 = $11,450

Year 4: $17,000

Year 5: $12,400

3 years + ($11,450/$17000)

3 years + 0.67years

3.67 years.

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