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Company $mathrm{X}$ is based in the United Kingdom and would like to borrow $$$ 50$$ million at a fixed rate of interest for five years in U.S. funds. Because the c...

Question

Company $mathrm{X}$ is based in the United Kingdom and would like to borrow $$$ 50$$ million at a fixed rate of interest for five years in U.S. funds. Because the company is not well known in the United States, this has proved to be impossible. However, the company has been quoted $12 %$ per annum on fixed-rate five-year sterling funds. Company $Y$ is based in the United States and would like to borrow the equivalent of $$$ 50$$ million in sterling funds for five years at a fixed rate of interes

Company $mathrm{X}$ is based in the United Kingdom and would like to borrow $$$ 50$$ million at a fixed rate of interest for five years in U.S. funds. Because the company is not well known in the United States, this has proved to be impossible. However, the company has been quoted $12 %$ per annum on fixed-rate five-year sterling funds. Company $Y$ is based in the United States and would like to borrow the equivalent of $$$ 50$$ million in sterling funds for five years at a fixed rate of interest. It has been unable to get a quote but has been offered U.S. ?ollar funds at $10.5 %$ per annum. Fiveyear govemment bonds currently yield $9.5 %$ per annum in the United States and $10.5 %$ in the United Kingdom. Suggest an appropriate currency swap that will net the financial intermediary $0.5 %$ per annum.



Answers

A company has an investment project that would cost $\$$10 million today and yield a payoff of $15 million in 4 years.

a. Should the firm undertake the project if the interest rate is 11 percent? 10 percent? 9 percent?
8 percent?

b. Can you figure out the exact cutoff for the interest rate between profitability and nonprofitability?

So while saying the question learns for them, moved to dance. And so let's see here that profitable loss is equal to $15 Divided by one plus. Want 11 to the power for which is equal to $9.88 minus $10 which is equal to minus $1,190 million. And the second one is profit or loss is equal to $15 divided by one plus .10 to the power for which is equal to 10 point $2,452 $10 which is equal to wine, $2,452 million. and the 3rd 1 is profitable. Laws is equal to $15 divided by one plus point 09 to the powerful, which is equal to 10 point $6,264 $10, which is equal to point $6,264 million. and the 4th 1 is profitable loss Which is equal to $15 Divided by one plus point 0 to the power for which is equal to 11 point 02 $5.4 $-10 which is equal to 1.0 $254 million. So increasing discount rate above 10% will make the investment unprofitable hands. The company must financial project at a lower rate at a rate lower than 10% in order to make a positive profit. So here is the full solution and definition that profitable losses equal to $15 divided by one plus 10.11 to the power four which is equal to $9.88 minus $10 which is equal to minus $1190 million. And the second one is profitable loss which is equal to $15 Divided by one plus .10. to the power for which is equal to $10.2452 $-10 which is equal $2.2,452 million. And the third one is profitable, losses equal to $15 divided by one plus 10.9 to the power for which is equal to $10.6264 minus $10 which is equal to $100.6264 million. And the fourth one is profitable losses equal to $15 divided by one plus 10.8 to the power four Which is equal to $11.0254 -10, which is equal to $1.025 million. So increasing discount rate above 10% will make the investment unprofitable. Hence the company must finance a project at a rate lower than 10% in order to make a positive profit. So I hope you better understand the full solution And and definition so for any further curation doubts I'm there for help. So thank you

So while seeing the question, let's for the move to the answer. So let's see here that profitable laws is equal to $15 divided by one plus .11 to the power for Which is equal to nine $88 $-10 Which is equal to -1190 million dollars. And the second one is profit or loss is equal to $15 Divided by one plus .10 With the powerful, which is equal to 10 $2,452 -10, which is equal to point 2452 million dollars. And the 3rd 1 is profit or loss is equal to $15 divided by one plus 109 to the power for which is equal to 10 point $6,264 $-10 which is equal to why $6,264 million. and the 4th 1 is profit or loss is equal to $15 divided by one plus .08. With a power four, Which is equal to 11 02 $5.4 $10, which is equal to 1.02 $5, million. So increasing discount rack above 10% will make that investment unprofitable. Hence the company must financial project act a rate lower than 10% in order to make a positive profit. So here is the solution and definition of the question. So here his first profit or loss is equal to $15 Divided by one plus .11 to the power for which is equal to $9.88 -10, which is equal to minus $1190 million. And the second one is profit or lost, which is equal to $15 divided divided by one plus 0.10 to the powerful, which is equal to 10 point $2,452 -10, which is equal to point $2452 million. And the third one is profit or loss which is equal to $15 divided by one plus 10.9 to the power for which is equal to $10.6,264 -10 which is equal to $0.6264 million. And the fourth one is profit and loss which is equal to $15 divided by one plus 0.8 to the power four which is equal to $11.254 minus $10, which is equal to 1.025, million. So increasing discount rate about 10% will make the investment unprofitable. Hence the company must Finance a project at a rate lower than 10% in order to make a positive profit. So I hope you better understand the full solution in the definition. So for any further curious and doubts I am there for help. So thank you.

Okay, guys, this is Chapter 27 problem. Three. So in this question were given that they're two bombs. Bond A pays $8,000 in 20 years. And Bondi here's $1,000 in 40 years. So the first part of questions asking us that the interest rate is 3% what is the current value of the bonds? So this was a net present value question, and the formula for net present value can be found on Page 5 65 the textbook. The formula is facts, which is the payment you get over one plus the interest rate to the power of and which is the number of years in the future that you're going to receive the payment equal to the Net present value of the first bond. We're going to receive $1,000 on an interest rate of 3% in 20 years, and this is going to equal for $1,020. You can't do this with the rule of 70 like the question that intimate questions says. But it's very easy to do this with formula. I'm so for Bond be it's gonna be 8,000 over one class. The interest rate to the power 40. And this is 2,000 and 20 right? This is bond be. And this is bond, eh? S O. Obviously bond be is worth less. And that's because you have to wait longer to receive the payment, which means because of inflates him in price changes. The value of the dollar and 40 years is worth less than the value of the dollar in 20 years, which is worth less than the value of the dollar today. So Part B then ask this if the interest rate changes to 7% plus the present value of each bond, which bonds changed the most, they were going to be using the same formulas and for buying any. It's $8,000 over one class 0.7 now to the power of 20 and this equals 2,000 and $67. And for bomb be. It's $8,000 over one last point of seven Power 40 and this is 537 so we can see that the 20 year bond is still worth more than the 40 year bond there. Now, which value has changed the mouth that this is just a simple percentage change from divinity bond. A. First they'll live the 2,067 minus the value of the interest rate in 3.5% which is 4,000 and 20 divided by 4,000 and 20. And this equals it's a minus 48.5% change for bond being I was getting the same thing 537 minus 1,000 and 20 over 2,020 equals minus 0.735 or minus 73.5%. So we see that the 40 year bond is more sensitive. The decrease in the prices Graydon the last part. It says to complete the sentence. That's in the question. The sentence is the value of a bond blanked 20. Interest rate increases and bonds with a larger maturity are blank, sensitive to change in the interest rate. Then, looking back to parts and B, we see that the value of bond decreases with the interest rate receded. The present value of the bonds, or higher to 3.5% rake and they are 7% rate. And that bomb, the longer maturity, are more sensitive. The 40 year bond decreases and price more when the interest rate increases from 40 3.5% to 70% of the 20 year Von Death. This was Chapter 27 problem three.

All right, We're given a pretty complicated expression here, and they're asking us to find the limit as n goes to infinity. Um, the question states that I is greater than G is a reasonable assumption. So if I is greater than G recognized that the fraction in brackets here one plus g over one plus I, you'd have a smaller number on top on a bigger number on the bottom. So we're really saying this fraction is in between zero and one. So as we take a number that's in between zero and one to the power of infinity as the limit states, this entire term actually just goes to zero. That just goes to zero. And really, we have are over I minus G times one minus zero and that just turns into are over. I minus G.


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