Question

Suppose a company owns a fancy 3D printer which costs $1500 to buy. The printer depreciates $200 per year.

(a) If the interest rate is 3 percent, what is the implicit rental price of the printer per year?

(b) Does your answer to part (a) depend on whether the company used its own money to buy the printer, or if it took out a loan? Why?

Suppose a newer edition of the 3D printer comes out for $2000. Because better technology is used, there is less depreciation; it only depreciates by $150 a year.

(c) Calculate the implicit rental price for the new edition of the printer. Which edition of the printer - old or new - has a larger implicit rental price?

(d) Suppose the interest rate was instead 5 percent, rather than 3 percent. Which edition of the printer - old or new - has a larger implicit rental price? Compare your answer with part (c), and comment on any difference.

Answer 1

The Intial Price of Printer = $1500, The depreciation- $200/year.

Lets assume the salvage value to be zero and using th straight line method of depreciation formula

Depreciation value= (Cost of the material- Salvage value) / Number of years (n)

200 = 1500- 0/ (n), n= 7.5 . n= 7.5 years

Using the interest rate of 3% per annum, the Final value of the printer will become

a) Final Value= Present Value (1+ r/100)^n, Final Value= $1500 (1+ 3/100)^7.5, Final Value = $ 1872.22

Therefore, the implicit rental price per year= $ 1872.22/7.5= $249.63 . Now the rent per month if asked will be = $249.63/12 = $ 20.80.

b) The answer does depend on interest rate prevailed as if the company invested its own money then the above return should be obtained from rent. If the Company takes loan, it may save the some amount in the interest part if the bank interest on loan is lower than the 3% and can rent out at a lower price as the bank interest is calculated on decreasing principal basis .

c) Now the he Intial Price of Printer = $2000, The depreciation- $150/year.

Lets assume the salvage value to be zero and using th straight line method of depreciation formula

Depreciation value= (Cost of the material- Salvage value) / Number of years (n)

150 = 2000- 0/ (n), n= 13.33. n= 13.33 years

Using the interest rate of 3% per annum, the Final value of the printer will become

Final Value= Present Value (1+ r/100)^n, Final Value= $2000 (1+ 3/100)^13.33, Final Value = $ 2965.85

Therefore, the implicit rental price per year= $ 2965.85/13.33= $222.49 . Now the rent per month if asked will be = $222.49/12 = $ 18.54.

The new version of the printer has low rental price compared to the older version.

d) If the Interest rate- 5% , then for the older intial price and number of years,

Final Value= Present Value (1+ r/100)^n, Final Value= $1500 (1+ 5/100)^7.5, Final Value = $ 2162.77

  Therefore, the implicit rental price per year= $ 2162.77/7.5= $288.36 . Now the rent per month if asked will be = $288.36/12 = $ 24.03

Therefore, it is evident that if the interest rate for the old version is 5%, then that rental price is higher than the new version rental price and the difference will be = $(288.36- 222.49)=$ 65.87 per year .