Question

brief explanation

Solve this problem using the incremental Benefit - Cost ration with, expected life of 10 years and rate of return of 10% Alternative A Initial cost $50,000 Annual maintenance cost $4,000 Estimated annual benefit $10,000 Alternative B Initial cost $30,000 Annual maintenance cost $3,000 Estimated annual benefit $9,000 a. Select A with B/C =1.14 b. Select B with B/C = 1.14 c. Reject A with B/C = 1.14 d. Select B with B/C = 0.14

Answer 1

Given that: Alternative A: Initial cost is $50,000 Annual maintenance cost is $4,000 Estimated annual benefit is $10,000. Alternative B: Initial cost is $30,000 Annual maintenance cost is $3,000. Estimated annual benefit is $9,000. Number of years is 10 Rate of return is 10%.

Benefit cost ratio: The benefit cost ratio can be calculated as follows: PV of benefit Benefit cost ratio PV of cost Present value of cost for alternative A can be calculated as follows: PV of cost-Initial investment + ( Annual maintenance costx P/ F @ 10%) 50,000+(4000 x 6.1445) 50,000+24,578 -74,578 Therefore, the present value of cost of alternative A is $74578

Present value of benefit for alternative A can be calculated as follows PV of benefit-Annual benefit x P/ F @ 10% -10,000x 6.1445 61,445 Therefore, the present value of benefit of alternative A is $61,445 Using Equation -1, the benefit cost ratio of alternative A can be calculated as follows 61.445 Benefit cost ratioa - 74,578 0.8239 Therefore, the benefit cost ratio of alternative A is0.8239

Present value of cost for alternative B can be calculated as follows: PV of cost-Initial investment + (Annual maintenance cost x P/ F @ 10%) - 30,000 +(3,000x 6.1445) 30,000+18,433.5 - 48,433.5 Therefore, the present value of cost of alternative B is S48.433.5 Present value of benefit for alternative B can be calculated as follows PV of benefit-Annual benefitx P/ F@10% 9,000x6.1445 55,300.5 Therefore, the present value of benefit of alternative B is S55,300.5

Using Equation -1, the benefit cost ratio of alternative B can be calculated as follows: 55,300.5 Benefit cost ratios 48.433.5 -1.1417 Therefore, the benefit cost ratio of alternative A is1.1417 The benefit cost ratio of alternative B is higher than alternative A and it showing positive value. Therefore, select option B with B/C ratio of 1.14. Therefore, the answer is option b

(Note: The P/F @ 10% taken from the compound interest table.)