Wilson Co. is considering two mutually exclusive projects. Both require an initial investment of $10,000 at t = 0. Project X has an expected life of 2 years with after-tax cash inflows of $6,000 and $8,500 at the end of Years 1 and 2, respectively. In addition, Project X can be repeated at the end of Year 2 with no changes in its cash flows. Project Y has an expected life of 4 years with after-tax cash inflows of $4,600 at the end of each of the next 4 years. Each project has a WACC of 11%. What is the equivalent annual annuity of the most profitable project? a. $1,345.50b. $1,346.30c. $1,361.52d. $1,376.74e. $1,411.15

d. $1,376.74

Explanation:

NPV of Project X is

Year Cash outflow/inflow Present value factor Present value

0 - $10,000.00 1 - $10,000.00

1 $6,000.00 0.900901 $5,405.41

2 $8,500.00 0.811622 $6,898.79

NPV $2,304.20

NPV of Project Y is

Year Cash outflow/inflow Present value factor Present value

0 - $10,000.00 1 - $10,000.00

1 $4,600.00 0.900901 $4,144.14

2 $4,600.00 0.811622 $3,733.46

3 $4,600.00 0.731191 $3,363.48

4 $4,600.00 0.658731 $3,030.16

Total $4,271.25

Formula for calculation of Equivalent annual annuity is given by:

C = r * (NPV) / (1 - (1+r) - n)

Applying the formula for project X, NPV = $2304,20

r = 11%, n = 2

Substituting the values in the above formula

C = 11%*$2304,20 / (1 - (1+11%) - 2

=$1345.38

Applying the formula for project Y, NPV = $4271.25

r = 11%, n = 4

Substituting the values in the above formula

C = 11%*$4271.25 / (1 - (1+11%) - 4

= $1376.74

Therefore, most profitable project is Y and its equivalent annual annuity = $1376.74.