Question

A project will cost $1,000 today and will pay back $100 one year from today (t=1), $200 two years from today (t=2), $500 three years from today (t=3) and $1,000 four years from today (t=4). If the required rate of return is 7%, answer question Q1 to Q5.

Q1: What is the present value of the future cashflow?

a)1578.62

b)1439.19

c)1374.25

d)1664.83

Q2: What is the NPV of the project

a)439.19

b)1439.19

c)578.62

d)1374.25

Q3: What is the IRR of the project?

a)21.75%

b)15.39%

c)16.84%

d)19.77%

Q4: What is the payback period of the project?

a)3.5

b)3.2

c)3.8

d)4

Q5: How long is the Discounted Payback Period

a)3.28

b)3.42

c)4

d)2.77

Answer 1

1)

Present value of future cashflow = 100 / (1 + 0.07)¹ + 200 / (1 + 0.07)² + 500 / (1 + 0.07)³ + 1000 / (1 + 0.07)⁴

Present value of future cashflow = 93.4579 + 174.6878 + 408.1489 + 762.8952

Present value of future cashflow = $1,439.19

2)

NPV = Present value of cash inflows - present value of cash outflows

NPV = 1,439.19 - 1,000

NPV = $439.19

3)

IRR is the rate of return that makes NPV equal to 0

NPV = -1,000 + 100 / (1 + 0.07)¹ + 200 / (1 + 0.07)² + 500 / (1 + 0.07)³ + 1000 / (1 + 0.07)⁴

Using trial and error method, i.e., after trying various values for R, lets try R as 19.77%

NPV = -1,000 + 100 / (1 + 0.1977)¹ + 200 / (1 + 0.1977)² + 500 / (1 + 0.1977)³ + 1000 / (1 + 0.1977)⁴

NPV = 0

Therefore, IRR is 19.77%

4)

Cumulative cash flow for year 0 = -1000

Cumulative cash flow for year 1 = -1000 + 100 = -900

Cumulative cash flow for year 2 = -900 + 200 = -700

Cumulative cash flow for year 3 = -700 + 500 = -200

Cumulative cash flow for year 4 = -200 + 1,000 = 800

200 / 1000 = 0.2

Payback period = 3 + 0.2 = 3.2 years

5)

Cumulative cash flow for year 0 = -1000

Cumulative cash flow for year 1 = -1000 + 93.4579 = -906.5421

Cumulative cash flow for year 2 = -906.5421 + 174.6878 = -731.8543

Cumulative cash flow for year 3 = -731.8543 + 408.1489 = -323.7054

Cumulative cash flow for year 4 = -323.7054 + 762.8952 = 439.1898

323.7054 / 762.8952 = 0.42

discounted payback period = 3 + 0.42 = 3.42 years