present value calculation) Dowling Sportswear is considering building a new factory to produce aluminum baseball bats. This project would require an initial cash outlay of $5,000,000 and would generate annual net cash inflows of $1,000,000 per year for eight years. Calculate the project's NPV using a discount rate of 9%.

The NPV is $534,819.11

Explanation:

The computation of the Net present value is shown below

= Present value of all yearly cash inflows after applying discount factor - initial investment

The discount factor should be computed by

= 1 : (1 + rate) ^ years

where,

rate is 9%

Year = 0,1,2,3,4 and so on

Discount Factor:

For Year 1 = 1 : 1.09^1 = 0.9174

For Year 2 = 1 : 1.09^2 = 0.8417

For Year 3 = 1 : 1.09^3 = 0.7722

For Year 4 = 1 : 1.09^4 = 0.7084

For Year 5 = 1 : 1.09^5 = 0.6499

For Year 6 = 1 : 1.09^6 = 0.5963

For Year 7 = 1 : 1.09^7 = 0.5470

For Year 8 = 1 : 1.09^8 = 0.5018

So, the calculation of a Present value of all yearly cash inflows are shown below

= Year 1 cash inflow * Present Factor of Year 1 + Year 1 cash inflow * Present Factor of Year 1 + Year 1 cash inflow * Present Factor of Year 1 + Year 1 cash inflow * Present Factor of Year 1 + Year 1 cash inflow * Present Factor of Year 1 + Year 1 cash inflow * Present Factor of Year 1 + Year 1 cash inflow * Present Factor of Year 1 + Year 1 cash inflow * Present Factor of Year 1

= $1,000,000 * 0.9174 + $1,000,000 * 0.8417 + $1,000,000 * 0.7722 + $1,000,000 * 0.7084 + $1,000,000 * 0.6499 + $1,000,000 * 0.5963 + $1,000,000 * 0.5470 + $1,000,000 * 0.5018

= $917,431.19 + $841,679.99 + $772,183.48 + $708,425.21 + $649,931.39 + $596,267.33 + $547,034.24 + $501,866.28

= $5,534,819.11

So, the Net present value equals to

= $5,534,819.11 - $5,000,000

= $534,819.11

We take the first four digits of the discount factor.