MY QUESTION: In this question provided, can you elaborate on the following: - ho

Question

MY QUESTION:

In this question provided, can you elaborate on the following:

- how you get the "Under Floating Rate" i.e. Rate = LIBOR%+2% => 6%

- regarding the PV Cash Flow equation, can you explain the difference between between fixed and floating? For example, why is .06 divided by whereas 1.06 is multiplied by the amount of terms.

ORIGINAL QUESTION:

A corporate treasurer believes interest rates are going to rise and decides to swap future floating rate payments for fixed rate payments. The firm is paying LIBOR+2% on $5 million in debt for the next two years with payments due semi-annually. LIBOR is 4%. The next payment is due in six months. Swapping involves exchanging LIBOR for fixed payments of596. The firm's cost of capital is 12% per annum with se compounding, If LIBOR rises by 50 basis points per six-month month, starting tomorrow, what is the present value of anticipated swap cash flows? mi-annual -$25,000 (cost savings) $24,808.64 (cost savings) +$24,808.64 (added cost) +$25,000 (added cost)

EXPERT ANSWER:

Under Fixed Rate

Rate =5% + 2% =7% pa or 3.5% half yearly

Interest on Debt per half-year =$0.035x5,000,000 =$175,000

Present Value of Cash Flows over next 2 years =$175,000x{(1-(1+0.06)-4)/0.06}

                                                                    =$175,000x3.4651

                                                                    =$606,393.48

Under Floating Rate

Rate =LIBOR% + 2% => 6% for HY1, 6.5% for HY2, 7.0% for HY3, 7.5% for HY4

Interest on Debt =$0.030x5,000,000 for HY1, 0.0325x5,000,000 for HY2, 0.035x5,000,000 for HY3, 0.0375x5,000,000 for HY4

=150,000 for HY1, 162,500 for HY2, 175,000 for HY3, 187,500 for HY4

Present Value of Cash Flows over next 2 years =$150,000/1.06 + 162,500/1.062 + 175,000/1.063 + 187,500/1.064

                                                                    =$581,584.79

PV Cash Flow change from Floating to Fixed = $606,393.48 - 581,584.79

                                                                    =$24,808.69

Hence, option-(c) is the right answer

Explanation / Answer

As current LIBOR is 4%..so LIBOR+2=6%

Both fixed and floating present value calculations are same..

In fixed, the PV=175000/1.06+175000/1.06^2+175000/1.06^3+175000/1.06^4=606393.48

Which is same as what the expert has written..In fixed, expert has shortened the calculations by using Geometric Progression

In fixed, as the payments are all same we can use Geometric Progression.

Geometric Progression is a series where the next term is some multiple * previous term. Or, it is a series in which e each term after first is found as multiplying previous one by fixed, non-zero number known as common ratio.

for example: a,ar,ar^2,ar^3..............

here we see all the terms follow same multiple=term/previous term=r, common ratio

Sum of a Geometric Progression is a(1-r^n)/(1-r) where n is the number of terms in the series

In our case as we see r=1/1.06 as all the payments are 1/1.06*previous payment

n=4

a=175000/1.06

So, the sum would be 175000*(1-1/.106^4)/(1-1/1.06)=175000/1.06*(1-1.06^-4)/0.06*1.06=175000*(1-1.06^-4)/0.06=606393.48

In floating, the payments are all different hence we can not use Geometric Progression

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