(a) On Jan 1, 2011, Detective Lester Freamon plans to retire from the Baltimore Police Department (BPD). The BPD is going to make him monthly payments for 20 years (240 payments in total). It will make alternating monthly payments of $10000 and $20000 (i.e., the first monthly payment (on Feb 1, 2011) will be $10000; the second will,be $20000; the third $10000; the fourth $20000 and so on). The relevant discount rate is 12% APR, compounded monthly. The present value of BPD’s retirement obligation to Det. Freamon is $1,400,000. If the present value of the monthly payments falls short of this figure, a one time payment will be made to Det. Freamon on Jan 1, 2011, to cover the difference.,Determine the amount of the one time payment to be made.,(b) Det. Freamon plans to invest half of the one time payment received on Jan 1, 2011 in Exxon corporate bonds and the other half in Google stock. Assume that Google has just paid the dividend of $15 per share on Jan 1, 2011 (just prior to buying the shares). The annual dividends (to be paid at the start of every January 1) are expected to grow at 10% (each year) for the next 5 years and then level off to a 2% growth rate (each year) indefinitely. On Jan 1, 2011, Exxon has corporate bonds on the market with face value of $1000 which mature in 10 years. The bond makes no payments for the first 3 years, then pays $100 every year over the subsequent 4 years, and finally pays $150 every year over the last 3 years (All payments are made by Exxon on January 1. The first $100 coupon,payment occurs on Jan 1, 2015). Assume that the present values of the shares and the bonds are calculated with 12% APR. How many Exxon corporate bonds and Google shares will Det. Freamon buy?,(Fractional quantities of each are allowed.)
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