Question

In: Finance

The Perth Mint (the government corporation that prints money and coin) had just produced a one...

The Perth Mint (the government corporation that prints money and coin) had just produced a one kilogram gold coin imbedded with a rare-red-argyle diamond. The mint values the coin at $1,000,000. A one kilogram of gold has a market value of approximately $50,000 while the news media values the rare diamond at $950,000.

1. If the gold and the diamond both increase in value at 2% per annum, how much will the coin be worth in ten (10) years' time?

11. Assume gold increases in value at the risk free rate estimated to be 1.7% and diamonds have an average expected annual rate of price increase of 4.5%.

How much will the cold coin be worth in ten years' time?

111. Would you consider the gold coin a good investment? Why or why not?

Solutions

Expert Solution

1. The following details have been provided:

Present Value (PV) of Gold = $50,000

Present Value of Diamond = $950000

Growth rate (g) = 2% per annum

Time period (t) = 10 years

Now, Value of Coin = Value of Gold + Value of Diamond

So, Value of Coin in 10 years = PV of Gold(1+ g)^t + PV of Diamond(1+g)^t

= 50,000(1 + 0.02)¹⁰ + 9,50,000(1+0.02)¹⁰

=50,000(1.02)¹⁰ + 9,50,000(1.02)¹⁰

Using calculator, we find the value of (1.02)¹⁰, it comes to 1.219

= 50,000* 1.219 + 9,50,000 * 1.219 = 60,950 + 1158050 = $1219000

The value of coin in 10 years will be $12,19,000

11. The value of the coin can be determined in a similar manner as the above. Just the growth rate for gold will 1.7% (g₁)and the growth rate for diamond will be 4.5% (g₂)

So, Value of Coin = Value of Gold in 10 years + Value of Diamond in 10 years

Value of Coin = PV of Gold(1+g₁)^t + PV of Diamond(1+g₂)^t

Plugging in the values, we get

Value of Coin = $50,000(1+0.017)^10 + $9,50,000(1+0.045)^10

Value of Coin = 50,000(1.017)^10 + 950000(1.045)^10

Using calculator we can find the value of 1.017^10, which will be 1.184 and 1.045^10 will be 1.553

So, Value of Coin = 50,000*1.184 + 950000*1.553

Value of Coin = 59200 + 1475350 = $15,34,550

So, the value of coin will be $15,34,550

111. Yes, I would consider gold coin as a good investment because it is one of the safer investment option as compared to investment in stock and mutual funds. Although the growth of value of gold coin might not be as high as stocks, it is considerable. Someone who wishes to keep his original investment safe and is satisfied with long term considerable growth, gold coins act as a good investment.

jeff jeffy answered 4 months ago

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