Time Value of Money

Case Study: ABC Wealth Advisors

As a newly recruited MBA in a financial consultancy firm, in order to test your knowledge of Time Value of Money $,$ you have been given the task of solving problems faced by various clients of the firm.

The first client for the day was Shubhman, a college student who has recently won a prize money of Rs$.1$ lakh in a quiz competition. He wants to invest the amount for a period of $5$ years so that he can use the amount from the investment for joining a cricket course. He wishes to know what would be the amount at the end of $5$ years if he earns an interest rate of $7\%.$

Ishan is the next client on the list. He is working with a KPO and expects to receive a bonus of Rs$.25000$ every year. He wishes to invest the amount for a period of $6$ years such that it accumulates to Rs$.2,40,000$ at the end of $6$ years. He wants to know the interest rate at which he must invest to meet his goal.

Prithvi is the third person on the list. He has just started his career. Expecting that his salary would increase at a certain rate every year, he worked out his savings on an average. He wants to invest Rs$.36000$ per year for the first $4$ years, Rs$.48000$ per year for the next $5$ years and Rs$.60000$ per year for $6$ years thereafter. He wants to know how much the amount would accumulate after $15$ years in order to make a real estate investment at that time. He wishes to invest in financial instruments offering a return of $7\%$ p$.$a$.$

Virat is the next client on the list. Virat had invested in his friend$$s business and received a share of Rs$.10$ lakh out of the profit. He wants to deposit the money in a bank for a period of $5$ years. He wants to know how much money he can draw every year so that there would be no balance left at the end of the period if the bank pays an interest of $7\%$ p$.$a$.$

The next client on the list is Surya. He is working as a sales executive in an MNC$.$ He received a sales incentive of Rs$.500000$ which he has invested in a financial plan offering a return of $12\%$ p$.$a$.$ He wants to know how many years would it take to double the money? And how many years to accumulate Rs$.15$ lakhs?

Jaddu, the next client is about to retire and he wants to receive pension every year. He expects to receive Rs$.12000$ per year for $8$ years and Rs$.48000$ per year thereafter. He wants to know the present value of the income stream if the discount rate is $10\%.$

Ashwin is the next client who has won a man of the match award. His sponsors offer him $3$ options: a$.$ a lump sum payment of Rs$.7\mathrm{.}5$ lakhs today; b$.$ Rs$.18$ lakhs to be received after $8$ years; c Rs$.1$ lakh per annum to be received in perpetuity; d$.$ Rs$.30000$ per month for a year and Rs$.5$ lakhs at the end of the year. Assume the cost of capital is $12\%$

Rituraj, the next client is to retire after $14$ years. He wants to invest in a retirement plan that would give him a perpetual income of Rs$.30,000$ from the beginning of the $15$th year. So$,$ he wants to know the amount he should invest now to meet his criterion if the interest rate is $8\%.$

Umran has just started his career and is keen on saving up for his retirement. He wishes to accumulate Rs$.3$ crores over a period of $20$ years. Mr$.$ Sharma advises him to invest in equity large cap funds which is expected to give an annualized CAGR of $12\%.$ Umran wishes to know how much he should be saving each month for the next $20$ years to generate the required corpus?

Washington$$s company has been offered a contract for the development and delivery of a solar powered military troop transport vehicle. The RFP provides all technical specifications and it stipulates that two working, economically feasible prototypes must be delivered in $4$ years, at which time you will receive your only customer payment $$ a single and final payment of Rs$.50$ million. Assume a reinvestment rate of $18\%$ for all the amounts received over the next $4$ years. Washington wishes to know :

a$.$ What lump sum amount should he be willing to accept today instead of the $$50$ million in $4$ years.

b$.$ Alternatively, what $4$ year receipts, starting a year from now, should he accept?

Kuldeep a car dealer offers car loans with $2$ different schemes. Scheme A offers $10\%$ discount on down payment of cash. Scheme B asks for a down payment of Rs$.18000$ and a monthly payment of Rs$.4100$ for $5$ years. If the cost of the car is Rs$.2\mathrm{.}5$ lakhs and the required rate of return is $9\%,$ what is the present value of the cash inflows from both the schemes?

Yuzi has just turned $35$ and has been saving for an around the world vacation. He wants to take the trip to celebrate his $40$th birthday. He has set aside as of today Rs$.9$ lakhs for such a trip. He expects the trip will cost Rs$\mathrm{.}15$ lakhs. The financial instruments that he has invested Rs$.9$ lakhs in have been earning, on an average, about $8\%.($You may ignore income taxes$).$

a$.$ Will Yuzi have enough money in that vacation account on his $40$th birthday to take the trip? What will be the surplus$/$shortfall in that account when he turns $40?$

b$.$ Yuzi says that he may be able to further fund the trip by making, starting today, $5$ annual contributions of Rs$.30,000$ at the end of every year to the account. If he adhered to that plan, how much will be in the account on his $40$th birthday.

Rohit is planning for his retirement. He is currently $35$ years old and plans to retire at the age of $55.$ Once he retires at the age of $55,$ he wishes to withdraw Rs$.8$ lakhs per annum for his consumption needs for the next $15$ years, ie till the age of $70.$ Each withdrawal shall be made at the beginning of the year and. How much should be the value of his investments when Rohit turns $55,$ to meet this retirement need. Rohit wishes to invest in an investment which will yield a $9\%$ return.

Mahi who is $40$ years old has retired and wishes to contribute Rs$.15$ lakh per annum to a charitable organization for the next $15$ years when he reaches the age of $60.$ He wishes to invest equal sums of money every year so that he can contribute to the charity He currently has Rs$.8$ lakhs in his bank account $.$ Assume that the investment earns an interest of $8\%$ per annu