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

YearCash outflow/inflowPresent 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

YearCash outflow/inflowPresent 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.

Explanation:

First, find the NPV of each project.

Using a financial calculator with "CF" function, input the following;

Project X

Initial investment; CF0 = -10,000

Yr1 cashflow; CF1 = 6,000

Yr2 cashflow; CF2 = 8,500

Interest rate; I/Y = 11%

then CPT NPV = 2,304.20

Project Y

Initial investment; CF0 = -10,000

Yr1 cashflow; CF1 = 4,600

Yr2 cashflow; CF2 = 4,600

Yr3 cashflow; CF3 = 4,600

Yr4 cashflow; CF4 = 4,600

Interest rate; I/Y = 11%

then CPT NPV = 4,271.25

Next, calculate equivalent annual annuity of each project;

Project X;

Present value; PV = -2,304.20

Total duration; N = 2

Interest rate per year; I/Y = 11%

Onetime future cashflow; FV = 0

then CPT PMT = 1,345.50

Project Y;

Present value; PV = -4,271.25

Total duration; N = 4

Interest rate per year; I/Y = 11%

Onetime future cashflow; FV = 0

then CPT PMT = 1,376.74

Therefore, equivalent annual annuity  of most profitable project is $1,376.74