An economic Analyst at TB2F Bank is trying to predict the central bank's next course of action regarding interest rates, which are now 3.5%. He believes that the Taylor rule will help him to do this. He has the following data: Neutral Rate = 4% Target inflation = 2% Current Inflation = 0.5% Long term expected GDP trend = 3% Expected 1yr GDP growth = 3.2% Question: What actions should Analyst expect from the central bank and what is driving that decision?
Taylor Rule: Target Rate = Neutral Rate + .5( Expected rate - GDP Trend) + .5(expected inflation - target) Target Rate = 4% + .5( 3.2% - 3%) + .5( 0.5% - 2%) Target Rate = 4% + 0.1% - 0.75% Target Rate = 3.35% The Analyst should expect the central bank to reduce rates from 3.5% to 3.35%. Even though GDP growth is strong relative to long term expectations, which would suggest a slight rate reduction, inflation is much lower than target. The Analyst should expect the Fed to reduce rates to drive inflation.
A stocks is currently priced at $14. It paid a $1 dividend last year and you expect this to grow at 5% annually. Your required rate of return is 15% and you are confident that you can sell the stock for $15 2 years from now. Calculate the value of this stock and explain whether or not you would invest.
Step 1 - Value the stock This requires the dividend discount model. Be careful, there is tiny trick here. PV of D1: D1/(1+r)^t = $1.05/(1.15)^1 = $0.91 ( A common mistake would be to use $1 as D1. However the questions states that $1 was last year's dividend. D1 represents next year's dividend, which we expect to grow by 5% vs last year) PV of D2: ($1.05*1.05)/(1.15)^2 = $0.83 PV of expected sales price: $15/(1.15)^2 = $11.34 Fair value of stock = $0.92 + $0.8 + $11.34 = $13.08 Step 2 - Make Investment Decision We have determined that the fair value of the stock is $13.06. However, the stock is now trading at $14. Based on our valuation, the stock is currently overpriced. We will not invest in the stock at this price. This is because we would not earn our required rate of return based on our dividend and future sale price assumptions.
Jeff starts a widget business by purchasing a widget machine with $5,000 of his own money. He depreciates it at 10% per year using the straight line method Each widget uses $1 worth of raw materials and he sells each for $1.50. After a year he has sold 10,000 widgets. Anne has an older, competing widget business, and sells 60,000 widgets annually, generating $72,000 in revenue and has a 20% gross margin. Questions: 1) How much depreciation should be charged and describe the impact on he Profit and Loss, and Balance Sheet 2) What can you infer about the differences between Jeff and Anne's business. Comment on profitability and competitive position.
Question 1: Depreciation expense = 10% of $5,000 = $500 $500 shows up as a expense on the P&L, reducing net income. The value of the widget machine on the asset side of the balance sheet is also reduced by $500. The shareholders equity side of the balance sheet is also $500 lower than it otherwise would have been as a result of reduced retained earnings, ensuring the balance sheet is still balanced. Question 2: Anne has a larger more mature business generating $72k in revenue while Jeff has generated $15k of revenue in his first year. However, Jeff's business has a gross margin of (1.50-1.00)/1.5 = 33% while Anne generates 20% of gross margin. This is explained by the fact that Anne sells widgets for $1.20 each vs Jeff's $1.50, and it cost her only slightly less to produce them, $0.96 vs Jeff's $1.00. Without more information we cannot comment on why this is the case. Anne does make widgets with slightly less expensive materials, however, unless customers perceive significant differences in quality between Jeff and Anne's widgets, it is difficult to imagine Jeff being able to continue to command such a high price for his widgets. On the other hand, Anne may have the opportunity to increase the price of her widgets and increase the profitability of her business, while still being the lower cost producer with the cheaper product.