Financial Calculations

Classified in Mathematics

Written at on English with a size of 2.36 KB.

1. Present Value of an Investment

15 Years Case

Present Value of the Investment = \$4,900 [ (1/0.08) − (1/0.08(1 + 0.08)^15)] = \$41,941.45

2. Effective Annual Rate (EAR)

EAR = (1 + (APR/m))^m − 1 If m becomes infinite, EAR = e^APR − 1

7% APR and quarterly compounding: EAR = (1 + (0.07/4))^4 − 1 = 7.19%

16% APR and monthly compounding: EAR = (1 + (0.16/12))^12 − 1 = 17.23%

11% APR and daily compounding: EAR = (1 + (0.11/365))^365 − 1 = 11.63%

3. Value of a Perpetual Stream of Payments

Present Value of the Perpetuity = (Payment/Interest Rate) Payment = \$2,500, Interest Rate = 0.061

PV of the perpetuity at date t=14 is \$2,500/0.061 = \$40,983.61. Discounting it back to date t=7, we should have PV7 = \$40,983.61/(1+0.061)^7 = \$27,077.12.

4. Bond Pricing

Bond Price = 35 * (1/YTM − 1/YTM(1 + YTM)^n) + Face Value/(1 + YTM)^n = \$837.11

5. Bond Yield

If interest rate increases to 9% Bond Price = 35 * (1/ 0.045 − 1/0.045(1 + 0.045)^4) + \$1,000/(1 + 0.045)^4 = \$964.12

Percentage Change in the Price of the Bond = (\$964.12 − \$1,000)/\$1,000 = −3.59%

6. Clean Price of a Bond

Clean Price = Invoice Price − Coupon Payment * (Days to Next Coupon Date/Days in Coupon Period) = \$950 − \$1,000 * 0.068/2 * 4/6 = \$927.33

7. T-Bill

1) Price of the Bill

Price = \$10,000 * (1 − 3.4% * 87/360) = \$9,917.83

2) Bond Equivalent Yield

Bond Equivalent Yield = (\$10,000 − \$9,917.83/\$9,917.83) * (365/87) = 3.48%

8. Stock Investment

Dividend Yield = \$10/\$540 = 1.85%

Capital Gain = (\$500 − \$540)/\$540 = −7.41%

Total Return = 1.85% − 7.41% = −5.56%

9. Margin Account

Margin = (\$400 * \$25 − \$400 * \$40 * 50%)/(\$400 * \$25) = 20%

If the maintenance margin requirement is 30%, she will receive a margin call.

Additional money required = \$8,000 − \$5,000 = \$3,000

Assume she has to sell N shares Value of remaining stock = (\$400 − N) * \$25 = \$10,000 − \$25N Remaining loan = \$8,000 − \$25N Margin = ((\$10,000 − \$25N) − (\$8,000 − \$25N))/((\$10,000 − \$25N) = 50% N = 240

Assume she can buy Y more shares Value of stock = (\$400 + Y) * \$50 = \$20,000 + \$50Y Maximum borrowing = \$8,000 + \$50Y Margin = ((\$20,000 + \$50Y) − (\$8,000 + \$50Y))/((\$20,000 + \$50Y) = 50% Y = 80