When Marilyn Monroe died, ex-husband Joe DiMaggio vowed to place fresh flowers o

Question

When Marilyn Monroe died, ex-husband Joe DiMaggio vowed to place fresh flowers on her grave every Sunday as long as he lived The week after she died in 1962, a bunch of fresh flowers that the former baseball player thought appropriate for the star cost about $4. Based on actuarial tables, "Joltin' Joe" could expect to live for 15 years after the actress died. Assume that the EAR is 9.6 percent Also, assume that the price of the flowers will increase at 3.2 percent per year, when expressed as an EAR. Assume that each year has exactly 52 weeks, and Joe began purchasing flowers the week after Marilyn died What is the present value of this commitment? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g.,32.16.) Present value $

Explanation / Answer

In one year there are total 52 weeks so in one year joe has to spend 52*price of flower

In year 1 price of flowers = 4

Price is increasing by 3.2%

So in year 2 price of flowers = 4*(1.032) = 4.13

In year 3 price of flowers = 4*(1.032)2 = 4.26

Similarly we can calculate price in all years

Joe is expected to live for 15 years

Yearly expense = Price of flowers*52

Therefore, Expense in year 1 = 4*52 = 208

Expense in year 2 = 4.13*52 = 214.66

Expense in year 3 = 4.26*52 = 221.52

Similarly we can calculate yearly expense for all years

Price and yearly expesne are in below table

Present value of commitment will be sum of present value of all yearly expense

Present value = yearly expense/(1+r)n, where r is expescted return and n is number of years

Present value of all commitments = Expense1/(1+r)1 +  Expense2/(1+r)2 + ............................. + Expense14/(1+r)14 +  Expense15/(1+r)15

Expensen is expense in year n

r is given as 9.6%

Now present value of commitment = 208/(1.096)1 + 214.66/(1.096)2 + ............................... + 313.26/(1.096)14 + 323.28/(1.096)15 = 1931.98

Present value of commitment = $ 1,931.98

Year Price Yearly expense 1 4.00 208.00 2 4.13 214.66 3 4.26 221.52 4 4.40 228.61 5 4.54 235.93 6 4.68 243.48 7 4.83 251.27 8 4.99 259.31 9 5.15 267.61 10 5.31 276.17 11 5.48 285.01 12 5.66 294.13 13 5.84 303.54 14 6.02 313.26 15 6.22 323.28

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