Question

Consider the following set of cash flows to be generated by an asset under consideration for investment.

            0                      1                      2                      3                      4                      5    years

            |---------------     |----------------   |----------------   |----------------   |----------------- |

            -$8000             $1500              $1500              $2100              $2100              $2275

The asset will cost $8000 to purchase. Assume a required rate of return of 9% per year, compounded annually.

A.        Calculate the net present value (NPV) of this set of cash flows.

B.        Calculate the internal rate of return (IRR) of the set of cash flows.

C.        Based on the NPV, should the company invest in this asset? Why or why not?

D.        Based on the IRR, should the company invest in this asset? Why or why not?

Answer 1

Cost of asset = $ 8000

So, cash flow in year 0 = -$8000 (negative sign indicates cash outflow)

Cash flow in year 1 = $1500

Cash flow in year 2 = $1500

Cash flow in year 3 = $2100

Cash flow in year 4 = $2100

Cash flow in year 5 = $2275

Required return = 9%

NPV is the sum of present value of all cash flows

To calculate the present value (PV) of a cash flow, we need to discount it by the required return.

PV = cash flow_n/(1+r)ⁿ,

where cash flow_n is cash flow in period n, r is required rate of return, n is time period

NPV = CF₀ + CF₁/(1+r)¹ + CF₂/(1+r)² + ................... + CF_n-1/(1+r)^n-1 + CF_n/(1+r)ⁿ

A.) Now, put all values in the NPV equation

NPV = -8000 + 1500/(1+0.09)¹ + 1500/(1+0.09)² + 2100/(1+0.09)³ + 2100/(1+0.09)⁴ + 2275/(1+0.09)⁵

Solving this, we get NPV = -$773.46

So NPV = -$773.46

B.) Internal rate of return (IRR) is the rate that make NPV of a project equal to zero.

To calculate IRR, we equate NPV equation to zero and the resulting 'r' is IRR

CF₀ + CF₁/(1+r)¹ + CF₂/(1+r)² + ................... + CF_n-1/(1+r)^n-1 + CF_n/(1+r)ⁿ = 0, by solving 'r' in this equation we will get as IRR

Now, putting all values in the IRR equation

-8000 + 1500/(1+r)¹ + 1500/(1+r)² + 2100/(1+r)³ + 2100/(1+r)⁴ + 2275/(1+r)⁵ = 0

Solving this we get 'r' as 5.47%

So, IRR = 5.47%

C.) If NPV is greater than zero then company should invest in asset as it is creating value for the company

In this case, NPV is -$773.46, which is negative

Therefore, company should not invest in the asset.

D.) If IRR is greater than required rate of return then company should invest in asset as it is earning more rate than required

In this case, IRR is 5.47%, which is less than required rate of return of 9%

Therefore, company should not invest in the asset.