Mathematics Homework Solutions

Theory of Numbers

The Lucas numbers Ln are defined by the equations L1 = 1 and Ln = Fn+1 + Fn-1 for each n ≥ 2 Prove that Ln = Ln-1 + Ln-2 (n ≥ 3) See attached file for full problem description.

Quantitative Methods

a. Decision Alternative b. Optimistic Approach c. Utility d. Constraint e. Objective Function f. Linear Programming g. Activities h. Consequence i. Game Theory j. Problem Formulation k. Lottery l. Decision Tree m. Immediate Predecessors n. Critical Activities o. Chance event ___ An unc ...continues

Extended DuPont Equation

Use the extended DuPont equation to provide a summary and overview of your firm’s financial condition. See attached file for full problem description.

Calculating Cash and other Accounting/Finance Variables

1. The Marchal Company is evaluating the proposed acquisition of a new machine. The machine's base price is $250,000, and it would cost another $15,000 to modify it for special use. The machine falls into the MACRS 3-year class, and it would be sold after 2 years for $75,000. The machine would require an increase in net work ...continues

Value of Warrant

Charles River Company has just sold a bond issue with 10 warrants attached. The bonds have a 20-year maturity, an annual coupon rate of 12.0 percent, and they sold at their $1,000 par value. The current yield on similar straight bonds is 15.0 percent. What is the implied value of each warrant?

Value of Operations

1. Hastings is interested in acquiring Vandell Corporation. Vandell has 1 million shares outstanding and a target capital structure consisting of 30% debt. Vandell's debt interest rate is 8%. Assume that the risk-free rate of interest is 5% and the market risk premium is 6%. Vandell's free cash flow is 2 million per year and ...continues

Cross Exchange Rate

A currency trader observes that in the spot exchange market, 1 U.S. dollar can be exchanged for 9 Mexican pesos or for 111.23 Japanese yen. What is the cross-exchange rate between the yen and the peso; that is, how many yen would you receive for every peso exchanged??

What is the 6-month forward exchange rate?

Six-month T-bills have a nominal rate of 7 percent, while default-free Japanese bonds that mature in 6 months have a nominal rate of 5.5 percent. In the spot exchange market, 1 yen equals $0.009. If interest rate parity holds, what is the 6-month forward exchange rate?

Price Change/Exchange Rate

Early in September 1983, it took 245 Japanese yen to equal $1. More than 20 years later that exchange rate had fallen to 108 yen to $1. Assume the price of a Japanese-manufactured automobile was $8,000 in September 1983 and that its price changes were in direct relation to exchange rates. a. Has the price, in dollars, of the au ...continues

Financial - Accounting Questions

1. The Hamlin Corporation has an inventory conversion period of 57 days, a receivables collection period of 35 days, and a payables deferral period of 25 days. Its annual credit sales are $5,000,000, and its annual credit purchases are $3,500,000. a. What is the length of the firm's cash conversion cycle? b. What is the fir ...continues

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