# pvsol - Solutions to Present Value Problems Present Value...

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Solutions to Present Value Problems Present Value: Solutions Problem 1 a. Current Savings Needed = \$ 500,000/1.110 = 192,772 \$ b. Annuity Needed = \$ 500,000 (APV,10%,10 years) = 31,373 \$ Problem 2 Present Value of \$ 1,500 growing at 5% a year for next 15 years = 18,093 \$ Future Value = \$ 18093 (1.08^15) = 57,394 \$ Problem 3 Annual Percentage Rate = 8% Monthly Rate = 8%/12 = 0.67% Monthly Payment needed for 30 years = \$ 200,000(APV,0.67%,360) = 1,473 \$ Problem 4 a. Discounted Price Deal Monthly Cost of borrowing \$ 18,000 at 9% APR = 373.65 \$ [A monthly rate of 0.75% is used] b. Special Financing Deal 17.98245614 Monthly Cost of borrowing \$ 20,000 at 3% APR = 359.37 \$ The second deal is the better one. Problem 5 a. Year-end Annuity Needed to have \$ 100 million available in 10 years= 6.58 \$ [FV = \$ 100, r = 9%, n = 10 years] b. Year-beginning Annuity Needed to have \$ 100 million in 10 years = 6.04 \$ Problem 6 Value of 15-year corporate bond; 9% coupon rate; 8 % market interest rate Assuming coupons are paid semi-annually, Value of Bond = 45*(1-1.04^(-30))/.04+1000/1.04^30 = 1,086.46 \$ If market interest rates increase to 10%, Value of Bond = 45*(1-1.05^(-30))/.05+1000/1.05^30 = 923.14 \$ The bonds will trade at par only if the market interest rate = coupon rate. Problem 7 Value of Stock = 1.50 (1.06)/ (.13 - .06) = 22.71 \$ Problem 8 Value of Dividends during high growth period = \$ 1.00 (1.15)(1-1.15^5/1.125^5)/(.125-.15) 5.34 \$ Expected Dividends in year 6 = \$ 1.00 (1.15)^5*1.06*2 = 4.26 \$ Expected Terminal Price = \$ 4.26/(.125-.06) = 65.54 \$ Value of Stock = \$ 5.34 + \$ 65.54/1.125^5 = 41.70 \$ Problem 9

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pvsol - Solutions to Present Value Problems Present Value...

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