Question

Use time value of money techniques to answer the following questions. Round all interest rate calculations to four decimal places. Round all dollar amounts to the nearest whole dollar. (1) TIME VALUE OF MONEY PROBLEMS Griggsville Company needs $3,000,000 for expansion of its manufacturing plant at December 31, 20X9. The company is able to earn a 5% annual return on its investments, compounded monthly. If the company begins investing in an account on January 1, 20X5 for this expansion, how much would the company need to deposit each month to this investment account in order to have the money it needs? William Griggsville will retire on December 31, 20X8 after 27 years with his present employer at the age of 58. Over this time period, Griggsville's individual retirement account (401(k)) has grown to $600,000. At the date of retirement, he is expected to live another 22 years. He has spoken with the employee benefits officer at his company, who has given him the following options for the payout on his retirement (ignoring income tax considerations). (a) (b) A one time lump sum payment on December 31, 20X8 in the amount of $600,000. An annual payment of $59,000, guaranteed for 22 years, to begin on the day that he retires, with no other payments after the 22 years. If he dies before 22 years, the payments will be paid to his estate. Which of the above options is the best for him if the retirement account earns 9% per year? Provide an appropriate explanation for your answer (3) Griggsville Company has surplus cash of $1,500,000 to invest. If the company can invest the cash for 6 years at 8% per year, how much will the company have at the end of 6 years under the following situations. (a) (b) Interest is compounded semiannually. Interest is compounded monthly.

Answer 1

(1) Savings horizon is 5 years hence 60 months. Interest rate is 5%. In order to get $3,000,000 after 5 years, monthly deposit required is $44,114 as calculated below:

B A 1 Annuity Payment C D E Payments at the end of each period 2 3 Amount of periodical payments is calculated using the formula PMT= (PV*r)/(1-(1+r)^-n] 4 Where PMT= Periodical payments required, 5 PV=Present value of future sum which is FV/(1+r)^n 6 n= Number of payments. 7 r= Rate of interest per period in decimals 8 All amounts in $ 9 Given that 10 Future value required FV= 3000000 No. of years (N) 11 Rate of interest (% p.a)=R= 5 No. of payments a year (t) Allan 13 Calculations: Value 0.004166667 15 Interest rate per period in decimals (r )= 16 No. of periods (n)= 60 17 19 Present Value of future amount (PV)= Formula Cell reference R/(100*t) D11/(100*G11) N*t O'G11*G11 (1+r)= 1+G15 (1+r)^n= G174G16 FV/(1+r)^n= D10/G18 (1+r)^-n= G17A-G16 [1-(1+r)^-n]= 1-G20 FV*r= G19*G15 (FV*r)/(1-(1+r)^-n] G22/G21 Rounded to 1.004166667 1.283358679 2337616.171 0.77920539 0.22079461 9740.067379 44113.70093 $44,114 23 Periodical payment required (PMT)=

(2): Present value of option (a) lump sum payment on 31 December 20X8 is $600,000

Present value of option (b) ie. Annual payment of $59,000 for 22 years with first payment on 31 December 20X8 is the present value of an Annuity Due, amounting to $607,242 as calculated below:

B C D 1 Present Value of Annuity Due (advance) Payments at the beginning of of each period 3 Present value of annuity is calculated using the formula PVA=P+ P*{[1-(1+r)^-(n-1)]/r]} 4 Where P= Periodical payments, 5 n= Number of payments. 6 r= Rate of interest per period in decimals All amounts in $ Given that 9 Periodical payments (P)= 59000 No. of years (N)= 10 Rate of interest (% p.a)=R= 9 No. of payments a year (t)= 11 11 12 Calculations: 13 Formula Cell reference Value 14 Interest rate per period in decimals (r)= R/(100*t) D10/(100*G10) 0.09 15 No. of periods (n)= N*t G9*G10 22 16 (1+r)= 1+G14 1.09 (n-1)= 18 (1+r)^-(n-1)= G164-G15 0.163698064 [1-(1+r)^-(n-1)]= 1-G17 0.836301936 (1-(1+r)^_(n-1)]/r= G18/14 9.292243733 21 Present value of annuity PV= P+P*{[1-(1+r)^-(n-1)]/r]} D9*G19 607242.3803 Rounded to $607,242 17 23

Since the option (b) have a higher present value, the same is advantageous for William Griggsville.

(3): Given that Amount of investment (P) = $1,500,000. Term of investment (N)= 6 years. Interest rate (R) =8%

Future value at the end of the term is arrived at using the formula FV=P*(1+r)^n

Situation (a): Compounded semiannually. Hence r= R/2= 8%/2 = 4%. n= N*2= 6*2= 12

Applying the given values in the formula, FV= $1,500,000*(1+04)^12 = $1,500,000*1.601032= $2,401,548

Hence the a value at the end of 6 years with interest @6% compounded semiannually is $2,401,548

Situation (b): Compounded monthly. Hence r= R/12= 8%/12 = 0.6667%. n= N*12= 6*12= 72

Applying the given values in the formula, FV= $1,500,000*(1+0.006667)^72 = $1,500,000*1.613502= $2,420,253

Hence the a value at the end of 6 years with interest @6% compounded semiannually is $2,420,253