The ABC Construction Company is considering the purchase of a diesel power shove
ID: 2720994 • Letter: T
Question
The ABC Construction Company is considering the purchase of a diesel power shovel to improve its productivity. The company finances the purchase by borrowing from a local bank with no origination fee. The principal will be repaid with the compounded interests (annual nominal interest rate: 10%) for 5 years. The bank compounds the financial charges semi-annually. The shovel, which costs $80,000, is expected to produce a benefit of $50,000 in the first year, and $4,000 less in each succeeding year for a total of five years (i.e.. benefit of $46,000 in the second year. $42,000 in the third year, continuing to $34,000 in the fifth year). The annual maintenance and operation cost of the equipment is $15,000 over 5 years. The company will sell the equipment with the expected resale price of $5,000 at the end of Year 5. Draw cash flow diagrams and determine whether the purchase is worthwhile at the MARR of 12%.Explanation / Answer
Loan Amount=80000 Effective Interest Rate with semi-annual compounding= (1+0.05)^2-1=10.25% Present Value of an annuity=PV=A*[(1+i)^n-1]/[(1+i)^n*i]. In the cited case for repayment of loan i=10.25% ,n=5, A=Equated annual repayments So, 80000=A*(1.1025^5)/(1.1025^5)*(0.1025) or A=80000*(1.1025^5)*(0.1025)/(1.1025^5)=8200 Particulars/Year 1 2 3 4 5 Loan Repayment (Outflow) (A) -8200 -8200 -8200 -8200 -8200 Benefits from the shovel (Inflow) (B) 50000 46000 42000 38000 34000 Annual Maintenance cost (Outflow) © -15000 -15000 -15000 -15000 -15000 Salvage value at the end of 5th year(Inflow) (D) 5000 Net cash flow=A+B+C+D 26800 22800 18800 14800 15800 Discounted cash flow @12% 23928.57 18176.02 13381.47 9405.668 8965.344 Net cash flow=Sum of all cash flow 73857.07 Since the cashflow is +ve at 73857.07 , it is worthwhile to invest in the shovel.
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