10. UMA age 33, works for a multinational looks after her own finances has a personal loan of Rs. 4 lakhs for 5 years with an EMI of Rs 9900 pm. She may receive a bonus shortly with which she plans to pay-off her personal loan. UMA wants to save for the education of her child. She wants to have a corpus ready in 7 years for this purpose and for this, she is planning to invest the bonus in XYZ Equity mutual fund. She had already invested Rs.40,000 in this XYZ fund three years back which is currently worth Rs.57720. The cost of child’s education is currently Rs.500000 and this is likely to go up by 10% every year. UMA has a short term goal of buying a car costing Rs 600000. The car dealer has given her two payment options – 1) Pay Rs. 600000 over 4 years with zero interest OR 2) Pay full amount as down payment now and get a 15% discount on this spot payment. UMA is also thinking of taking retirement in 20 years. But she wants to be sure that she receives regular income from her investments so that she can meet her essential expenses. For this she is scrutinizing a perpetual annuity that will pay her Rs 300000 every year from age 50 onwards at a yield of 6%. For this she is required to invest Rs. 11800 for 20 years in this annuity plan. UMA is also interested in spending her retirement life in a city apartment and is thinking if she can afford it ? The down payment for this apartment is Rs 1200000. For this, UMA plans to invest Rs. 22000 per month in a debt fund which will give her a return of 7% pa. She also believes that she will receive salary increments in the next few years which will allow her to save more and pay an EMI of Rs 55000 per month. She has decided to restrict the mortgage to 5 years. The cost of property currently is Rs 60 lakhs. The home loan rate is 7.5% and the inflation rate in the economy is 6.5%.
The car dealer has given her two payment options – 1) Pay Rs. 600000 over 4 years with zero interest OR 2) Pay full amount as down payment now and get a 15% discount on this spot payment. Which among these two options UMA should opt? Risk free rate as 6%.
Explanation:
Lets assume risk free interest rate as 6%.
Now UMA has two options
1) Invest 6 Lakhs in 6% risk free investment and take 12500 every month to repay Car Loan. Remaining amount shall keep on earning interest. How much amount will be left in the scheme after repayment of Loan?
2) Pay upfront and get 15% discount. Invest the discount amount in same 6% risk free investment for a period of 4 years. What is the amount at the end of 4 years?
Compare these two and see which is higher. That option is the best one.
Option 1 – Interest Free EMI Option. Invest Rs 6 Lakhs in 6% risk free investment.
Calculate monthly effective rate of interest = =1.06^(1/12)-1
Monthly effective rate of interest = 0.004867551
Calculate number of months Rs 12500 can be taken from the corpus using NPER formula.
=NPER(E26,-12500,600000,0,0) = 54.8
So 12500 can be taken from the corpus for 55 months.
Loan term is 48 months. So extra amount that can be withdrawn from the corpus even after paying loan is Rs 12500 * 7 months = Rs 87,500
Option 2 – Pay upfront and get 15% discount. Invest 15% discount amount in 6% risk free investment.
Car amount Rs 600000. 15% discount = Rs 90000
Rs 90,000 invested in 6% risk free asset class for 4 years = FV(6%,4,0,-90000)
Rs 90,000 invested in 6% risk free asset class for 4 years = Rs 1,13,623
Option 2 gives better return. Hence UMA should opt for Option 2. She should pay upfront and get discount.