Question

Question 1 A loan repayment plan is scheduled to be made as 10 uniform monthly payments of $1,500. The first repayment is expected to take place on May 30th. Subsequent repayments will take place at the ends of each subsequent month. For simplicity, assume that each month is precisely 30 days. The loan has a nominal annual interest rate of prime rate + 2.5%. If the prime rate, set by the lending bank, is currently 3.95%. Assuming that the prime rate remains constant throughout the loan repayment period, what is the annual nominal interest rate? a. Given the nominal interest rate from [a), if compounding is daily, what is the effective monthly interest rate? b. If the loan was received on April 30th, and given the effective monthly interest rate from [b] what is the maximum that can be borrowed? c. If the loan was received on January 30th instead, and the waiting period from this date to April 30th was interest-free, i.e., grace period, would that change the maximum amount that can be borrowed compared to the amount from [c]? d. If the loan was received on January 30th with no grace period and given that repayment plan and interest rates remain the same, what is the maximum that can be borrowed? e. If now the loan is to be received on April 30th, but prime rate goes up on July 30th by 0.50%, what is the maximum amount that can be borrowed. Compounding is still daily, and repayment plan is the same as before. f. g. If l inputs in [f] remain the same but compounding now is monthly, what is the maximum amount that can be borrowed? Question 2 An organization is considering the purchase of new machines to automatically conduct some quality control tasks. The machines are expected to save production cost which is given below as Annual Income. The machines are expected to be part of the production process for 5 years. The company has a minimum attractive rate of return (MARR) of 10%. The following data is available for these new machines Alternative Initial Annual Annual Operation andSalvage value $5,000 $7,500 $6,500 $2,200 Cost 28,000 9,000 $950 65,000 $16,000 $1,200 40,000 $12,500 $1,100 35,000 $9,000 $1,000 Income Maintenance costs a. Calculate the Net Present Worth (NPW) of each alternative b. Did you identify any infeasible alternative? c. Calculate the Internal Rate of Return (IRR) of each alternative d. Rank alternatives based on initial cost. e. Using incremental IRR analysis, what is the best alternative? f. Using results from [a] what is the best alternative?

Answer 1

Amount in Dollars No. of Periodic Payments Amount of Periodic Payments Type in timing Days in Each Month 10 1500 End of the period 1) Calculation of the Nominal Annual Interest Rate As per the Problem Nominal Annual Interest Rate Prime Interest Rate + 2.50% 395% 6.45% 2.50% Compounding Basis Calculation of the Effective Monthly Rate: For the calculation of Effective Monthly rate we calculate effective annual rate first EAR - Daily 2) (where 6.45% r= o645 (Where е.0645-1.06666) 1.06666 -1 6.66% EAR Monthly Effective Rate (1+EAR)/N 1 (1+EAR2 1 (Where Compounding is monthly N- 12) 1.06666" (1/12)-1 0.005392 - 0.5392175 %

3) Number of Periods - Payment Amount - Monthly rate 10 PMT 1500 0.539 % Amount That can be borrowed PV- ???? PV PMT Present Value Factor Annuity (.5392 %, 10 Periods) 1500 * 14564.57 Answer PV- PV- (Using Calculator or Excel) 9.709717 The Loan maximum can be granted for the PV of the Amount That is 14565 Dollars Alternative approach to calculate the effective monthly rate Continous compounding means to compounding to each day 6.45% 360 Days 0.0001792 (1+ o.o001792) 30 1 1.005388991 0.00538899 0.539 (Where this method is simple but does not give accurate result and has not been chosen)