Case $2$: Integration of Movements

in Prices, Inflation, and Exchange

Rate

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INFLATION, EXCHANGE RATES AND INTEREST RATES

Assume the domestic rate of inflation in South Africa has been $6$ percent per year

for the past three years, but the rate is expected to decrease by $0\mathrm{.}5$ percentage points

each year for the next two years until it reaches $5$ percent. Then, it is expected to

remain at that level in the future. The inflation rate in Japan has been $1$ percent per

year last year, but the rate is expected to decrease by $0\mathrm{.}2$ percentage point each year

for the next three years until it reaches $0\mathrm{.}4$ percent. Then it is expected to remain at

that level in the future. The price index for both South Africa and Japan in year $1$ is

$1.$

The currency of South Africa is the Rand and that of Japan is the Yen. Assume that

the market exchange rate in Year $1$ is $0\mathrm{.}10$Rand$/$Yen$.$

The nominal one$-$year interest rate for Rand loans is $9\mathrm{.}72$ percent as of Year

$1,$ with an expectation that the rate of inflation will be $5\mathrm{.}5$ percent the next year.

Assume that the real exchange rate between the two countries will remain at the

same level until Year $7.$

Assignment:

Prepare a table that contains the following information:

$1.$ The projected price index for South Africa from Year $1$ to Year $7.$

$2.$ The projected price index of the Japan from Year $1$ to Year $7.$

$3.$ What is the real exchange rate as of Year $1?$

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$4.$ Using the assumption that the real exchange rate remains constant over the

future $7$ years, what are the projected nominal exchange rates between Year $2$

and Year $7?$

$5.$ What is the real rate of interest as of Year $1$ in South Africa?

$6.$ Assuming that the real rate of interest remained constant over the next $7$ years,

forecast the annual nominal interest rates in South Africa that would be

consistent with the real rate of interest and the projected rates of inflation?

$7.$ Suppose the world price of a Personal Digital Assistant $($PDA$)$ that South

Africans buy from Japan is $10,000$ Yen per unit in Year $1.$ It is expected that

the real price of PDA$$s will decrease by $10$ percent a year, from Year $2$

onward, for the following $7$ years. What do you expect it to cost to South

African consumers in Rand price $($nominal$)$ in Year $6?$

$8.$ Suppose a South African firm obtained a $2\mathrm{.}5$ million Rand loan in Year $2,$ and

the loan principal is to be repaid in equal installments over the following $5$

years. The interest accrued over the previous year is also paid in the current

year. What would be the amount of interest expense paid each year over this

five$-$year period, expressed in the prices of Year $2?$ Estimate the annual tax

savings per year $($i$.$e$.$ in Year $2$ prices$)$ that will accrue to this company given

that it is subject to a corporate flat tax rate of $40\%.$ What would be the annual

savings under conditions of an expected rate of inflation of zero over the entire

period? Compare and comment on the differences in tax saving of the withand$-$without$-$inflation situation and the impact on the financial net present

value $($NPV$)$ of the activity. The real discount rate is $4\%.$

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$9.$ Suppose that instead of the real exchange rate between the Rand and the Yen

being held constant over time, it is expected that the Yen will appreciate

relative to all other currencies, including the Rand, by $2$ percentage a year

over the period from Year $2$ to Year $7.$ What would you expect the real and

nominal interest rates now to be from Year $2$ until Year $7$ on a Japanese Yen

loan made to the same South African business as described in question $8?$

What is the amount of real interest expense measured in Rand expressed in

the price level of Year $2$ for an equivalent Yen loan that is equivalent in value

to $2\mathrm{.}5$ million Rand in Year $2?$ What is the annual value of the foreign

exchange capital gain or losses associated with this foreign $($Japanese$)$ loan

over its repayment time?

$10.$Suppose, again, that this South African company has the following cash flow

profile, and that accounts receivable are estimated to be at $50\%$ of sales,

accounts payable to be at $10\%$ of operating costs $($material purchases $+$ direct

labor costs$),$ and cash balances to be at $10\%$ of sales.

$$ Cambridge Resources International Inc. $20224$

Year $2$ Prices Real Cash flow $($Rand$)$

Year $2345678$

Sales

revenues $3,500,0003,500,0003,500,0003,500,0003,500,0003,500,000$

Material

purchases $1,200,0001,200,0001,200,0001,200,0001,200,0001,200,000$

Direct

labor costs $40,00040,00040,00040,00040,00040,0000$

a$.$ Using a real discount rate of $4\%,$ and calculating the present values of the

following cash flow items, evaluate their impact on the cash flow statement

of this company under the condition of zero inflation and under the condition

of $10\%$ annual constant inflation rate

$$ Cash balances

$$ Accounts payable

$$ Accounts receivable

b$.$ Using the first$-$in$-$first$-$out $($FIFO$)$