Question

Q1. Your organization has developed a new product (let us call it A) which is 1000 dollars more expensive to purchase as compared with a similar product now available in the market (let us call it B). B currently costs 8000 dollars to purchase. The operating cost of A is however lower: 300 dollars per year. B costs 400 dollars per year to operate. Assume that the customers of these products base their purchase decisions on money considerations alone.

How much rebate you will have to offer in order to induce the customers to purchase A (instead of B) if the discount rate is 4 percent, and each product has an infinitely long useful economic life? (your answer must be rounded off to the nearest dollars, i.e., no decimal places)

Answer 1

Price of A = $9,000

Price of B = $8,000

Discount Rate = 4%

Operation cost of A = $300 per year

Operation cost of B = $400 per year

As operation cost of A is $100 less than B which means if we calculate present value of $100 per year for lifetime and substract it from $1,000, that should be the rebate amount.

Present value of Saving from product A in year 1 is (100 / 1.04^¹)

Present value of Saving from product A in year 2 is (100 / 1.04^²)

Present value of Saving from product A in year 3 is (100 / 1.04^³)

Present value of Saving from product A in year n is (100 / 1.04^ⁿ)

Saving of Sum of present value of machine A = (100 / 1.04^¹) + (100 / 1.04^²) + (100 / 1.04^³) + ................ + (100 / 1.04^ⁿ) which forms a geometric series with infinite period

Sum of GP series = [a / (1 - r)] where a is the first term = (100 / 1.04^¹) while r is ratio of two consecutive terms which is 1 / 1.04

Thus, sum of GP series = {(100 / 1.04^{^1}) / [1 - (1 / 1.04)]} = 100 / 0.04 = 2,500

As present value of saving of $100 from product A for lifetime is $2,500 and it cost $1,000 extra than product B, there should not be any rebate on product A or salesman should explain the benefit of extra $1,500 you will save while purchasing product A.