# Present Value Problems - Corporate Finance - Solved Quiz, Exercises for Corporate Finance. Alliance University

PDF (14 KB)
4 pages
1000+Number of visits
Description
Present Value Problems, Current Savings, Annuity, Future Value, Annual Percentage Rate, Monthly Rate, Discounted Price Deal, Special Financing Deal, Value of Bond are points of this solved quiz. These are for my friends.
20 points
this document
Preview3 pages / 4

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 Expected Rate of Return = (1000/300)^(1/10) - 1 = 12.79%

Problem 10 Effective Annualized Interst Rate = (1+.09/52)^52 - 1 = 9.41%

Page 1

Solutions to Present Value Problems

Problem 11 Annuity given current savings of \$ 250,000 and n=25 = 17,738.11\$

Problem 12 PV of first annuity - \$ 20,000 a year for next 10 years = 128,353.15\$ PV of second annuity discounted back 10 years = 81,326.64\$ Sum of the present values of the annuities = 209,679.79\$ If annuities are paid at the start of each period, PV of first annuity - \$ 20,000 at beginning of each year= 148,353.15\$ PV of second annuity discounted back 10 years = 88,646.04\$ Sum of the present values of the annuities = 236,999.19\$

Problem 13 PV of deficit reduction can be computed as follows –

Year Deficit Reduction PV 1 25.00\$ 23.15\$ 2 30.00\$ 25.72\$ 3 35.00\$ 27.78\$ 4 40.00\$ 29.40\$ 5 45.00\$ 30.63\$ 6 55.00\$ 34.66\$ 7 60.00\$ 35.01\$ 8 65.00\$ 35.12\$ 9 70.00\$ 35.02\$

10 75.00\$ 34.74\$ Sum 500.00\$ 311.22\$

The true deficit reduction is \$ 311.22 million.

Problem 14 a. Annuity needed at 6% = 1.89669896 (in billions) b. Annuity needed at 8% = 1.72573722 (in billions)

Savings = 0.17096174 (in billions) This cannot be viewed as real savings, since there will be greater risk associated with the higher-return investments.

Problem 15 a. Year Nominal PV

0 \$5.50 \$5.50 1 \$4.00 \$3.74 2 \$4.00 \$3.49 3 \$4.00 \$3.27 4 \$4.00 \$3.05 5 \$7.00 \$4.99

\$28.50 \$24.04 b. Let the sign up bonus be reduced by X. Then the cash flow in year 5 will have to be raised by X + 1.5 million, to get the nominal value of the contract to be equal to \$30 million. Since the present value cannot change,

X - (X+1.5)/1.075 = 0 X (1.075 - 1) = 1.5

Page 2

Solutions to Present Value Problems

X = 1.5/ (1.075 -1) = \$3.73 million The sign up bonus has to be reduced by \$3.73 million and the final year's cash flow has to be increased by \$5.23 million, to arrive at a contract with a nominal value of \$30 million and a present value of \$24.04 million.

Problem 16 Chatham South Orange

Mortgage \$300,000 \$200,000 Monthly Payment \$2,201 \$1,468 Annual Payments \$26,416 \$17,610 Property Tax \$6,000 \$12,000 Total Payment \$32,416 \$29,610 b. Mortgage payments will end after 30 years. Property taxes are not only a perpetuity; they are a growing perpetuity. Therefore, they are likely to be more onerous. c. If property taxes are expected to grow at 3% annually forever,

PV of property taxes = Property tax * (1 +g) / (r -g) For Chatham, PV of property tax = \$6000 *1.03/(.08-.03) = \$123,600 For South Orange, PV of property tax = \$12,000 *1.03/(.08-.03) = \$247,200

To make the comparison, add these to the house prices, Cost of the Chatham house = \$400,000 + \$123,600 = \$523,600 Cost of the South Orange house = \$300,000 + \$247,200 = \$547,200

The Chatham house is cheaper.

Problem 17 a. Monthly Payments at 10% on current loan = 1,755.14\$ b. Monthly Payments at 9% on refinanced mortgage = 1,609.25\$ Monthly Savings from refinancing = 145.90\$ c. Present Value of Savings at 8% for 60 months = 7,195.56\$ Refinancing Cost = 3% of \$ 200,000 = \$6,000 d. Annual Savings needed to cover \$ 6000 in refinancing cost= 121.66\$ Monthly Payment with Savings = \$ 1755.14 - \$ 121.66 = 1,633.48\$ Interest Rate at which Monthly Payment is \$ 1633.48 = 9.17%

Problem 18 a. Present Value of Cash Outflows after age 65 = \$ 300,000 + PV of \$ 35,000 each year for 35 years =

707,909.89\$ b. FV of Current Savings of \$ 50,000 = 503,132.84\$ Shortfall at the end of the 30th year = 204,777.16\$ Annuity needed each year for next 30 years for FV of \$ 204777 = 1,807.66\$ c. Without the current savings, Annuity needed each year for 25 years for FV of \$ 707910 = 9,683.34\$

Problem 19 a. Estimated Funds at end of 10 years:

FV of \$ 5 million at end of 10th year = 10.79\$ (in millions) FV of inflows of \$ 2 million each year for next 5 years = 17.24\$ - FV of outflows of \$ 3 million each year for years 6-10 = 17.60\$ = Funds at end of the 10th year = 10.43\$

b. Perpetuity that can be paid out of these funds = \$ 10.43 (.08) = 0.83\$

Page 3

Solutions to Present Value Problems

Problem 20 a. Amount needed in the bank to withdraw \$ 80,000 each year for 25 years = 1,127,516\$ b. Future Value of Existing Savings in the Bank = 407,224\$ Shortfall in Savings = \$ 1127516 - \$ 407224 = 720,292\$ Annual Savings needed to get FV of \$ 720,292 = 57,267\$ c. If interest rates drop to 4% after the 10th year, Annuity based upon interest rate of 4% and PV of \$ 1,127,516 = 72,174.48\$

Problem 21 Year Coupon Face Value PV

1 50.00\$ 46.30\$ 2 50.00\$ 42.87\$ 3 50.00\$ 39.69\$ 4 50.00\$ 36.75\$ 5 50.00\$ 34.03\$ 6 60.00\$ 37.81\$ 7 70.00\$ 40.84\$ 8 80.00\$ 43.22\$ 9 90.00\$ 45.02\$

10 100.00\$ 1,000.00\$ 509.51\$ Sum = 876.05\$

Problem 22 a. Value of Store = \$ 100,000 (1.05)/(.10-.05) = 2,100,000\$ b. Growth rate needed to justify a value of \$ 2.5 million,

100000(1+g)/(.10-g) = 2500000 Solving for g,

g = 5.77%

Page 4

no comments were posted