D8 - fx B D E F G H j K L M N R s T V w X Y 1 2 3 Basic Time-Value of Money Problems Total Number of Questions: 31 4 1a. What would the future value of $500 be after 5 years at 10% compound interest? 5 6 7 7 8 N 1 PV PMT 5 10% $500 $0 FV = 9 10 11 12 13 14 1b. At 10% simple interest? $50.00 Annual interest Total interest 15 = 5*10 but use cells in the forumula N 1 PV PMT 5 10% $500 $0 16 FV = 2. Suppose you currently have $3,000 and plan to purchase a 3-year certificate of deposit (CD) that pays 2% interest compounded annually. How much will you have when the CD matures? N 1 PV PMT 2% $3,000 $0 FV = 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 3a. Suppose a U.S. government bond promises to pay $3,000 three years from now. If the going interest rate on 3-year government bonds is 4%, how much is the bond worth today? N I PMT FV 3 4% SO $3,000 PV = 3b. How would your answer change if the bond matured in 5 rather than 3 years? 34 35 36 37 38 39 40 41 N I PMT FV 5 4% $0 $3,000 PV = 3c. What if the interest rate on the 5-year bond was 6% rather than 4%? 5 42 43 44 45 46 N 1 PMT FV 6% $0 $3,000 PV = 4a. How much would $1,000,000 due in 100 years be worth today if the discount rate was 3%? N I 1 PMT FV 100 3% SO $1,000,000 PV = 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 4b. If the discount rate was 20%? N 100 20% SO $1,000,000 PMT FV PV = D8 F K L X 63 64 65 66 67 68 69 70 71 72 - fx B D E H J M N R S T V w Y 5a. The U.S. Treasury offers to sell you a bond for $600. No payments will be made until the bond matures 10 years from now, at which time it will be redeemed for $1,000. What interest rate would you earn if you bought this bond for $585.43 N 10 PMT $0 PV $600.00 FV $1,000 5b. What rate would you earn if you could buy the bond for $550? N PMT PV FV 10 SO $550.00 $1,000 73 74 75 76 77 78 79 80 5c. For $900? N PMT PV FV 81 10 SO $900.00 $1,000 6a. Roberts Corporation earned $0.70 per share in 1999. Ten years later, in 2009, it earned $1.62. What was the growth rate in Roberts Corporation's earnings per share (EPS) over the 10-year period? 82 83 84 85 86 87 88 89 N PMT PV FV 10 SO $0.70 $1.62 E F G H 1 K L M N o R S T V w Y B D J 6b. If EPS in 2009 had been $1.00 rather than $1.62, what would the growth rate have been? 91 92 93 94 95 96 97 98 99 N PMT PV FV 10 SO $0.70 $1.00 7a. How long would it take $1,000 to triple if it were invested in a bank that pays 6% per year? (Hint: For these type of problems use the "NPER" Function) 1 PMT PV FV 6% SO $1,000 $3,000 N= 100 101 102 103 104 105 106 107 108 109 7b. How long would it take if the rate was 10%? 1 PMT PV FV 10% $0 $1,000 $3,000 N = 110 111 112 113 114 115 116 117 118 119 8a. What is the PV of an ordinary annuity with 12 payments of $200 if the appropriate interest rate is 10%? N 1 PMT FV 12 10% -$200 SO PV = 121 122 8b. What would the PV be if the interest rate was 4%? N 1 PMT FV 12 4% -$200 $0 PV = 123 124 125 126 127 128 129 130 131 132 8c. What if the interest rate was 0%? N 1 PMT FV 12 0% -$200 SO PV = 8d. How would the PV values differ if we were dealing with annuities due? 133 134 135 136 137 138 139 140 Parta N 12 1 10% PMT -$200 FV $0 PV $1,499.01 Part b N 12 1 4% PMT -$200 FV $0 PV = Partc N 12 1 0% PMT $200 FV $0 PV 141 142 143 9a. Suppose you inherited $1,000,000 and invested it at 5% per year. What is the most you could withdraw at the end of each of the next 10 years and have a zero balance at Year 10? N N 1 PV FV 10 5% $1,000,000 SO PMT = 9b. How would your answer change if you made withdrawals at the beginning of each year? 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 N I PV FV 10 5% $1,000,000 $ $0 PMT = 10a. If you had $100,000 that was invested at 8% and you wanted to withdraw $10,000 at the end of each year, how long would your funds last? 1 PV PMT FV 8.0% $100,000 $10,000 So N = 10b. How long would they last if you earned 0%? 1 PV PMT FV 0.0% $100,000 -$10,000 SO 170 171 N = 172 11a. What's the future value of $100 after 3 years if the appropriate interest rate is 5%, compounded annually? N I PV PMT 3 5% $100 $0 FV = 11b. Compounded monthly? 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 N I PV PMT 36 0.42% $100 SO FV = 12a. What's the present value of $100 due in 3 years if the appropriate interest rate is 6%, compounded annually? N 1 PMT FV 3 6% $0 $100 PV = 12b. Compounded monthly? N 1 PMT 199 36 0.5% $0 $100 200 FV PV = 13. A bond that matures in 10 years has a par value of $1,000, an annual coupon payment of $60; its market interest rate is 9%. What is its price? Years to maturity Annual payment Par value Going rate, rd 10 $60 $1,000 9% Value of bond = 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 14. A bond that matures in 12 years has a par value of $1,000 and an annual coupon of 12%; the market interest rate is 8%. What is its price? Years to maturity Coupon rate Annual payment Par value Going rate, rd 12 12% $120 $1,000 8% Value of bond = 220 221 222 223 224 225 226 227 228 229 15. Halley Enterprises' bonds currently sell for $950. They have a 7-year maturity, an annual coupon of $85, and a par value of $1,000. What is their yield to maturity? Hint: Find using the RATE function Years to maturity 7 Annual payment $85.00 Current price -$950.00 Par value = FV $1,000.00 YTM = Required rate, rd: 16. Last year a firm issued 22-year, 9% annual coupon bonds at a par value of $1,000. Suppose that one year later the going rate drops to 6%. What is the new price of the bonds assuming that they now have 19 years to maturity? 231 232 233 234 235 236 237 238 239 240 241 242 Years to maturity Coupon rate Annual payment Par value Required rate, rd 21 9% $90 $1,000 6% Value of bond = 243