Question

Botany Bay Inc. a maker of casual clothing, is considering four projects shown in the following table. Because of past financial difficulties, the company has a high cost capital of 14.6%.

Table.

Initial investment Project A: $49,200 Project B: $100,100 Project C: $79,400 Project D: $180,500
Year            Cash inflows          
1   $19,200   $35,000   $19,400   $100,700
2   $19,200   $52,000   $40,000   $81,000
3       $19,200   $50,900   $59,200   $59,300

a) calcualte the NPV of each project using a cost capital of 14.6%

b) Rank accetable products by NPV.

c) Calulate the IRR of each project and use it to determine the highest cost of capital at which all of the projects would be acceptable.

Answer 1

a). NPV = PV of Cash Inflows - PV of Cash Outflows

NPV_A = $19,200/1.146 + $19,200/1.146² + $19,200/1.146³ - $49,200

= $16,753.93 + $14,619.48 + $12,756.97 - $49,200

= -$5,069.63

NPV_B = $35,000/1.146 + $52,000/1.146² + $50,900/1.146³ - $100,100

= $30,541.01 + $39,594.43 + $33,819.25 - $100,100

= $3,854.69

NPV_C = $19,400/1.146 + $40,000/1.146² + $59,200/1.146³ - $79,400

= $16,928.45 + $30,457.25 + $39,201.09 - $79,400

= $7,319.68

NPV_D = $100,700/1.146 + $81,000/1.146² + $59,300/1.146³ - $180,500

= $87,870.86 + $61,675.94 + $39,400.42 - $180,500

= $8,447.22

b) Only B,C and D will be accepted as they have positive npv. In order of higher NPV first, the ranking will be

Project D, C and B.

c) IRR is the rate at which NPV is 0.

Project A:

Put the following values in the financial calculator,

CF0 = -49,200; C01 = 19,200; F01 = 3; Press IRR, then CPT, which gives, 8.32%

Project B:

Put the following values in the financial calculator,

CF0 = -100,100; C01= 35,000; F01 = 1; C02 = 52,000; F02 = 1; C03 = 50,900; F03 = 1; Press IRR, then CPT, which gives, 16.76%

Project C:

Put the following values in the financial calculator,

CF0 = -79,400; C01= 19,400; F01 = 1; C02 = 40,000; F02 = 1; C03 = 59,200; F03 = 1; Press IRR, then CPT, which gives, 19.19%

Project D:

Put the following values in the financial calculator,

CF0 = -180,500; C01= 100,700; F01 = 1; C02 = 81,000; F02 = 1; C03 = 59,300; F03 = 1; Press IRR, then CPT, which gives, 17.66%

Highest possible cost of capital equals lowest IRR, hence 8.32%