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3 years ago

The spot USD /GBP rate is 1.5711. The1 year t-bill rate in the US is .19%. The 1 year rate in the UK is 0.39%.

Business

1 answer:

mojhsa [17]3 years ago

8 0

Answer:

Spot USD/GBP rate = 1.5711

(a) 1 year USD/GBP forward rate:

= [Spot rate × (1 + Domestic currency interest rate)] ÷ (1 + foreign currency interest rate)

= [1.5711 × (1+0.19%)] ÷ (1 + 0.39%)

= 1.56797, which means the USD will be at a forward premium

b) The observed 1 year forward rate is 1.60 which differs from the ideal forward rate.

This means an arbitrage opportunity exists here.

c) I would sell GBP forward for 1 year @ 1.60.

This means that I will receive USD 1.60 for every 1 GBP I sell instead of 1.56797 that is the ideal deal.

This is how I would take advantage of the arbitrage opportunity.

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1. A new furnace for your small factory will cost $27,000 to install and will require ongoing maintenance expenditures of $1,500

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Answer:

payback 3.29 years

NPV 87,158.55

Explanation:

PO 27,000

Cash flow saving Y1

2400 x 3.5 = 8,400

expenditures (1,500)

net savings 6,900

Cash flow saving Y2

The price will increase 0.5

6,900 + 2,400 x 0.5 = 8,100

Cash flow saving Y3 to Y20

The price will increase 0.5

8,100 + 2,400 x 0.5 = 9,300

We have an annuity of 18 years for 9,300 cash

And then we have a cash flow of 6,900

and another of 8,100

$C \times \frac{1-(1+r)^{-time} }{rate} = PV\\$

C = 9,300

r = 8%

time = 18

$9,300 \times \frac{1-(1+0.08)^{-18} }{0.08} = PV\\$

PV = 87,158.55

Now this values are years into the future, so we need to bring them to present day.

$\frac{Principal}{(1 + rate)^{time} } = PV$

year 1 principal 6,900

6,900/1.08 = 6,388.89

year 2 principal 8,100

$\frac{8,100}{(1 + 0.08)^{2} } = PV$

PV= 5,915.64

year 3 annuity 87,158.55

$\frac{87,158.55}{(1 + 0.08)^{3} } = PV$

PV= 69,189.27

cash flow - investment = net present value

69,189.27 + 5,915.64 + 6,388.89 - 27,000 = 54,493.8

The payback will be the time perdion when the project recovers it initial cost:

we first add the income from the irregular years and subtract from the investment

6,900 + 8,100 = 15,000

27,000 - 15,000 = 12,000

then we use the general formula investment/cash flow per year

12,000/9,300 = 1.29

the project need the first two years and then 1.29 years

2 + 1.29 = 3.29 years

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Why?

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